Ok Let's take a look.
I was going to start talking about the their cultural relative to their interactions with other Astartes through the Deathwatch, which I would like to still talk about. But I think I should start more with background information.
I think that's a good idea to exemplify how they interact with other chapters. If they act like Thrawn did when he was in the Imperial Military proper, it'd be an interesting point of friction. You could even have their unique mutations be commented on by other more 'puritan' Astartes members negatively, but that entirely depends on whether you want to include that kind of commentary in your work.
Yeah I read a Deathwatch book and realized that a brief story of the chapter's interactions there is the perfect venue for describing how the chapter develops relationships for good or ill with other chapters. You are absolutely right, the inevitable conflict with more puritanical chapters, and by extension some sects of the Inquisition.
Other than that a cultural example is great. Due to the nature of the Deathwatch and it's role, it'd be hard to have this kind of work be front and center when talking about the chapter, especially when the Deathwatch members are sworn to secrecy - which is slightly idiotic as an aside, considering the nature of the Astartes and their role in 40k - when returning to their chapters. You'd end up telling a Deathwatch story that had a member of your chapter in it, as opposed to the story of your chapter with a sidebar or commentary on one of it's brethren's time in the Deathwatch.
I was definitely thinking of it that way, as a story of a member of the chapter, doing his vigil and interaction with other Astartes of chapters he may or may not know, developing bonds with some, butting heads with others. Basically the mini story i have in mind would be in the section stating they commit brothers to the Deathwatch and talks about a brother's service there that developed relationships and a new tradition for the chapter's brothers that join it, regarding their relationships there and 2 relic Crescent-pattern power maces made by the chapter that is now in the Deathwatch armory.
Specifically, I think I might change their lineage to be spliced geneseed between Vulkan and the II Primarch, which is technically feasible and would tie the mystery backstory together better. The Carcharadons are suspected of having spliced geneseed of Corax and Cruze after all. I am also thinking of expanding on their founding through a connection to an Astartes organization called the "Azure Chimeras" that have something to do with the II Legion, but I need think about it more. I think I would make these stories come to light in more recent times with the whole primaris marines thing going on, as it seems to be a logical time for more lineage information to emerge. I think this route might better develop the chapter idea as a whole and give a better baseline for their overall culture.
Right out of the gate I'll state I'm not a fan of mixed geneseed. Things like this were traditionally only done during, for example, the cursed founding and most of those chapters met with unfortunate ends. It's heretical in the extreme outside of sanctioned events like that as well.
I get it, you aren't wrong that it is exceedingly rare and only at special direction. However, there are enough examples of chapters, some cursed as you've said, some alive, that have geneseed suspected to be derived from either, loyalists of the traitor legions, spliced geneseed, or possibly Lost Legions, that the idea is plausible even if it is near impossible. In researching the Lost Legions and the feasibility of the idea, there is evidence that at least part of those legions likely survived in loyalist legions. Recently, it has been made clear that the Lost Legions geneseed was preserved, and theoretically, could be used, and may have been at the direction of the Emperor or his personal representative. Thus it is plausible, that either at the direction of the Emperor or his personal representative, or even unknowingly, that a current chapter could have Lost Legion geneseed. I guess I thought of it as, the chapter could have been an early, and for the reasons above, likely unique, experiment with using the Lost Legion geneseed and splicing it with a clearly loyalist geneseed, to attempt to prevent any corruption. Plus, there are many examples of chapters having their history, especially their lineage, sealed or purged for any number of unknown reasons.
Narratively speaking, it's got to be specifically tied to the makeup of the story of the chapter, like how the Soul Drinkers story is for a large part dominated by them not being who they thought they were, and the narrative springing from there. In any other respect it never feels necessary and in most cases simply feels like it's 'rule of cool', to try and make something unique without actually writing them to be so, relying on the crutch of something like 'mixed geneseed' or 'lost in the warp' or simply 'dark secrets', rather than actually writing something compelling.
I'll be honest, I was not originally thinking of using a Lost Legion in this at all, but then I occurred to me that it might allow me to develop a unique legion lineage and culture with greater freedom. So yes, it is meant to be used in order to develop story and concept. The chapter as it is now it a bit too, generalist more than cookie cutter, for me. I do not want nor intend to use vagueness to create the illusion of coolness or complexity. I intend to use this geneseed and connection to create a chapter that is unique, has personality and clearly develops and changes through its history. I want the general, semi cookie cutter chapter it sort of currently is, to not be the same chapter it is when I talk of in the current M41. It is not going to be so in the extreme that is it unrecognizable, rather that it has evolved. A chapter that is of 5th Founding (technically earlier by my story, maybe 3rd) needs a proper history. So again, I hear your concerns and they are valid, but bare with him on that front. I think your feedback is helping me develop something that can work, I would not even try this if I felt I could not think of enough concepts for it to be meaningful.
Don't get the cart before the horse. Write something that you think is a compelling story and see what springs from building that road, rather than dropping down a bunch of pretty statues and writing your way around them, forcing people to look at the statues rather than enjoying the drive on your road, if that makes sense.
A very good point to keep in mind! It will prob not be the first time someone has to remind me to walk before I run. 
This also applies to the 'azure chimeras' which naming wise, feels a little bit on the nose, as well as the second legion links. It'd be better to have something like that subtly implied in passing, but never stated anywhere if you were going to do it. If it were me, I'd also cloak it in suspicions around the Alpha Legion. On this I'd ask Ace Debonair for some tidbits of advice, considering his Knights Oracular are back and are Alpha Legion Infiltrators LOL, I am Alpharius? Is it too soon? Alpha Legion hunting specialists.
Sorry, "on the nose" in a good way or a bad way? I did choose the II over the XI because, it seems, not by much mind you, that there is slightly more barebones known on II. Also, since I was inspired by elite units of the legions and my obsession with ancient tech, it seemed to me the Emperor was somewhat favorable to the earlier legions in those regards, so it would make more sense for me to choose II for that reason. Also, the earlier geneseeds supposedly tend to be, well before the heresy as far as I know, tended to be more pure, so if a Lost Legion geneseed was used, it would make more sense to use the II? I looked at a long article on the Lost Legions and only thought of a name that fit within the sort of physical-relative-the-rest-of-the-text length of the II legion's name (apparently some document had it redacted in it in the lore). I guess I tried to keep from diving too deep into making a II legion by leaving further specifics desired if you will, but perhaps its not as successful.
Let me know more what you are imagining in terms of cloaking it in AL suspicion, because honestly, I have a chapter that basically is loyalist AL already called the Ellipsis Chapter in the Liber. And I do not want this chapter connected to AL, so I would prefer to avoid them, as much as I love the AL. Regardless, perhaps Ace might have some ideas on working the mystery better either way, I will ask him to take a look here.
Story of a company discovering a long lost legion armory with a dormant fellblade. Techmarine touches fellblade suddenly partial awakens its machine spirit, techmarine uses his devices to interact with machine spirit, which states in text "right of the inheritors, son of the chimera." basically leads the realization that for some reason the fellblade will only respond to those of its original legion or their gene-line, which as far as I know is not entirely unheard of for particularly revered and old machine spirits. Leads marines to realize it somehow knows they descendants of its original legion, they see if lists their legion or parent chapter in it. Machine spirit does not list whether it is a legion or chapter, but appears to be property of the "Azure Chimeras" confirming previously found vague references to the Knight Wardens be sired by the "Azure Chimeras" whatever they are. Basically another piece to the puzzle and a convenient way to give them some archeotech.
This falls into the same camp as above. You're getting attached to particular individual golden bricks and expecting them to form key structural components of the wall that is your chapter, when they'd just crush under expansion.
You are right, I am trying to jump ahead. Keep reminding me!
I'll explain. I think having a set of ideas for unique parts of the chapter are fine, but should be far, far less specific. Instead of this mini-story about a fellblade, just have one word "Archeotech" and leave it at that.
I suppose what it is, isn't actually important to the mini story. I could def just do that and if I wanted to just make a named fellblade in a misc war material section that has nothing to do with the story.
When you begin writing any story, you should typically start with broad strokes. It's fine to have a concept in your head for it, but start developing that idea as broadly as possible.
Example: I want to write a story about one of my Astartes. I begin with; a man is born, he lives, he dies. That's your basic beginning, middle and end. A story has to have those elements and while an IA is not a narrative story per-se, I view it as being the 'story' of your chapter. It covers their beginnings, how they're founded. Their middle years, their trials, tribulations and how they have been formed by these experiences. Finally their 'end' which is where you write your conclusion as to the character and state of the chapter and where they're poised to go as of the 'current' in stasis moment of the 40k timeline.
As I develop his story I flesh it out with each successive pass. I'll add his name, his tribe or birthplace. Then briefly mention the trials he suffered to become an Astartes before moving on to his early career, before finally heading to his death, or where the story will leave him.
If you keep developing that character long enough, you can pull a moment, battle, campaign, crisis or whatever you want from his life and you will have everything you need to write a story about it. You have his character, what challenges he's overcome and how that defines him.
This is how video game, movie and narrative franchise 'bibles' are developed as well, even if some of those are more a collection of ideas and development from multiple authors along the way.
Any time you dive too deep into hyper-specifics, you're getting the aforementioned cart before the horse.
Again, a good reminder. I am creative and a good writer in most things, but I know from experience that I am not good at narrative writing or whatever reason. So I appreciate the advise
Your chapter is founded. Your chapter overcomes challenges put before them and it defines their character, and culture. Your chapter and it's status at the end of the current 40k timeline, including consequences of their actions and character set up before.
This is def what I need to do to have a chapter that, as I said above, evolves through its history.
"The Murder of the Stars" - a cataclysmic event involving Necrons and a Ctan shard and the destruction of a moon that leads to them getting their chapter badge a reoccurring theme of crescents.
Not sure about the crescents, I'd need to know more about the event, but Necron ships tend to be croissant lmao sorry, crescent shaped in nature and I find it odd that a chapter would adopt the symbol of a xenos race they're fighting, even if it is just in ship aesthetics, unless the crescent existed in their symbology before hand.
Funny enough, I am glad you said that, but I was thinking in terms of the event destorying a moon such that all that remained was a crescent, it didn't even occur to me that Necron ships are also crescents.
That said, a cataclysmic event based around the Necrons is really cool and fitting right in with current 40k lore.
Yea I have to do alot more research on this first. If I remember correctly, there was some evidence that the Imperium encountered very early awakening Necrons or Necrons that forgot to sleep or something, but didn't know what they were, long before the official first contact with the Necrons. I need to see how early that actually was. Essentially the idea is that the chapter encounters the Necrons, likely a Ctan Shard, on some moon, they battle, and the Ctan Shard destroys the moon in its death, leaving a charred crescent, all that is left. The chapter memorialized this achievement and struggle by adopting the crescent moon as a theme and on their chapter sigil. I think, I will modify my original thinking in a manner that will work better with new ideas, but I will put that later on here.
Chapter Fortress Monastery being a 40k version of the "Hand of Thrawn" with certain advanced manufacturing capabilities, might modify the idea from being solely planet-side to being a starfort hidden as a planet-side base, but Murder of Stars event leads to it being back in space? Not sure.
I'm not sure, you have to be extremely careful how you do this. Older and first or second founding chapters can get away with something similar, but their inherited equipment and infrastructure is far different to a newer chapters.
Ah I see your concern, I have not communicated what I meant by this. No worries, I am not making them a Dark Angels copy or something ridiculous like that. See below.
You also need to think about the logistics of it. The larger the manufacturing presence you have, the more bodies you need to run it as well as materials needed to pump out production. Secondly, given the relatively low number of Astartes in a chapter, even with Guillimans new reforms, and the again relatively low attrition rate of Astartes in battle (think of the fact that most tactical marines are a hundred years old at least, as well as being the chapters backbone of fighting men), 'large' manufacturing facilities are fairly redundant.
Astartes chapters need to have a measure of self-sufficiency, this is true. Let's compare this to the real world, while I know the scale is different and operationally things change because of that, but stick with me here.
What I was thinking, and obvious did not communicate, was a fortress monastery that has some limited forging abilities that most chapters would not, mostly with power armors. I like certain marks of older armor and there is evidence that a few chapters have the ability to forge them still. Other than that, it would mostly be the standard forging, not a major factory. It also would work with the chapter being big on artificing due to their connection to the Salamanders. Idea may need modifying but I think my lack of clarity may have created a fear that it was more than it was.
A special forces group will have armorers in tow, but they won't have any local gun-manufacturing as part of the unit, or even division as a whole. They will have some extremely capable and knowledgeable members, but not all of them know their weapons as well as you might think, despite them being very proficient with them.
(Hell, Larry Vickers despite being as knowledgeable as he is has made a couple of asinine statements before regarding some firearms that he's been raked over the coals for, despite being a former Delta operator.)
Given how small a unit is, they need to be provided with the ability to repair and refit their weapons and keep them working. Where an Astartes chapter differs is in scale, since they also have to maintain working operation of powered armour, small arms, void-craft, atmospheric craft, transports and landers, tanks and so on and so forth. This means their operation of scale for the good operation of all of their assets naturally increases and to take a link out of their logistical nightmare of a supply chain, being able to manufacture on a limited scale greatly offsets some of this dependence upon the Mechanicus.
But just how much do you need to manufacture for your two to three-thousand strong special forces division?
I know this is a bit of a rant, so my apologies for that, it's just I see this pop up a lot in 40k lore and fan projects like IA's.
On the other side of the coin, I'd perhaps frame it as a Great Crusade era Astartes forge ship, and it's ability to manufacture is perhaps more efficient than modern forges, the alloys are stronger, the forging and milling tools more precise. It allows gear to be maintained to a higher standard than is possible with modern forges, but also gets you out of being a mary-sue with an ability to create your own GC era super-heavy tanks for your chapter out of the blue.
I think I can modify this idea and make it work with the Murder of the Stars event. Again, I have to do my research to see that it can work with the Necron lore, but, what if that event destroyed their original homeworld? And their fortress monastery partly survived due to its shielding, and was rebuilt to be similar to Ramilles star fort (because Imps and bloody STCs) with those forges I talked about above? Plus that would not only link concepts, but show evolution in the chapter.
Also, if I do that I could also rework the reason for the blue skin. It would change from being the natives having light blue skin that darkens with the geneseed implantation, to, the result of the II legion geneseed combining with Vulkan's. Because, if they changed homeworlds, the original idea doesn't work. This solution to that problems gives another reason to have the II legion, rather conveniently.
Deal with an Iron Hands successor chapter that is essentially an unusual quid pro quo, allowing the Knight Warden chapter's artificers and techmarines to examine the single suit of exceedingly rare Gorgon pattern Termi armor possessed by that Iron Hands successor. Leads to a centuries long project by the Knight Wardens' artificers and techmarines developing a Gorgon pattern inspired new terminator armor pattern (possibly named Chimera pattern). Non-combat prototype would exist by the present and idea would be modified to be intended for the new Primaris Marines that are slowly replacing the Firstborn. Intended for limited number of field testing versions to go into production over the early decades of Era Indomitus by 1st company veterans. Thinking of it as a limited production model for an utlra elite "Chimeran Dreadknights" unit, akin to some of the specialist elites of the Legions.
I'd stay away from this. I personally don't see it happening on a few levels. Again you're delving into hyper-specifics, but that aside I think all suits of Gorgon armour are unique to the Iron Hands themselves, extremely closely guarded as a secret, considering a lot of what the Iron Hands have done/are doing is tech-heresy in the extreme.
To round it out, it's not known so far as I'm aware if there are any suits left, since the majority of the suits were deployed with the Avernii Clan, which were wiped out at the Dropsite Massacre, though I could be wrong as Iron Hands lore isn't my strong-suit.
Also, do you really want to make your chapter unique by taking something that's unique to another chapter?
On top of that the Chiss as far as I'm aware aren't huge proponents of cyborgs or heavy use of cybernetics.
So I have to explain the reasoning for this, and I see its a bad idea, but perhaps I can take the reasoning for it to make a better idea that doesn't involve Gorgon termis. I love the look of the Gorgon-pattern termi armor and I also love the specialist termi units of the legions. So I want to make my own custom termis, but realize I have a problem because they havent had a new pattern in ages and now basically everything firstborn is being phased out. But maybe the forge fortress monastery idea above and chapter craftsmanship can solve this. Maybe, with the chapter's preference for close combat they were dissatisfied with some primaris marine armors, like Aggressor and Inceptor armors, so decided to create a new suit of Mark X armor that is more similar to termi armor of old, but with the advances of modern tech. Seems to solve the problem without breaking the rules doesn't it? And Cawl is into new ideas, so its not so far fetched I think.
Also thinking of making a successor chapter (Talons Mordant is a working name atm) of either the Knight Wardens, or "Azure Chimeras" that will be trained by veterans from many chapters, making it difficult to trace their origins until they discover it themselves. However, they will only be II Legion geneseed not combined like the Knight Wardens. This other chapter will be quite new, with many primaris marines, focused on legion style recon squads, marksmanship and swordsmanship, using guerilla and ambush tactics to weaken enemies before hitting them with shock assaults by assault marines and terminators (although I am thinking of giving them no termis). Their regular work behind enemy lines will lead them to discover their lineage and stronger connection to the Knight Wardens, and maybe work into this story arc as well. Maybe they and the Knight Wardens are each geneseed experiments done at the orders of the Emperor? Anyway, they will be publicly directed by either the High Lords or Lord Commander of the Imperium to hunt for Fabius Bile, as he becomes a growing concern thanks to information provided by the Inquisition (and yes this mostly because I hate Bile and any Slaanesh worshipers).
Unless you're as talented and capable as Ace (most aren't, I'm certainly not, much as I might try), I'd stick to fleshing and rounding out this chapter first before jumping into anything else, as you'll end up doing both chapters a disservice when things inevitably change on both ends and it becomes a mess.
By all means keep the idea around and even work on it a little as an overall concept, but wait till this one has some concrete foundations before you jump ship, at least in my opinion.