I shall give you one more up on this one and say that I feel like Sancho, being as old as she is, may well know how to play chess already even if she didn't remember as her Don Quixote persona. Like if the true Don Quixote had it as one of his many hobbies/interests and had all his Bloodfiends learn how to play, too, so that he'd have people to play against.
I enjoy the thought of Yi Sang seeing Don going to play against Sinclair like she had been doing before, and then her sitting down to play against him herself and soundly beating him. Leaving him more than a little gobsmacked.
Outis steps in to challenge her and is also completely taken aback by how easily she beats her. Outis then proceeds to spend several days plotting out multiple strategies and dedicating herself to annihilating her in chess as revenge.

Absolutely adore them.
Their whole meet-cute being Kali mistakenly kidnapping him because she thought he was someone else and then him sticking around because he got into their cause. Just imagine Kali's utter embarrassment when she learns he'll be working with them from now on. She's mortified. She swiped him up off the street by sheer accident and now she has to face him every day.
Then the gradual build-up of trust, getting to know each other. Nobleman who's never known need a day in his life giving all his wealth to the cause that Kali who comes from nothing wants to believe in so much. The little ways they're breaking down each others' walls from the different ways they grew up until something finally gives.
I like to think that when Gebura and Chesed recall their past lives in the Library, they might look back on those days a little bittersweetly. Knowing how much they grew closer but also seeing the flaws in how they used to be together. I think they'd still think on those times fondly, though.

I don't feel any particular way about trans Sinclair hcs of any variety tbh. Besides positive-neutral, I suppose.
Generally I hc Sinclair as a cis dude, which is how I most often portray him in my writing. So I'll admit that I've not put a lot of in-depth thought about Sinclair being trans personally, simply because its never been applicable to the ways in which I write him.
However, I have seen other peoples' art and writing which portray trans Sinclair, including transfem, in some very interesting ways that I wouldn't have conceived of simply because that's not the way that I write Sinclair. And I think that kind of breadth of creativity from others done out of love for a character to be shared can bring about a lot of wonderful work.
I guess, ultimately, I'd say my answer to this question is that it isn't really a matter of how I "feel" about the idea (even though I will say I do Not feel badly about the idea in the slightest!). Because how I personally feel doesn't matter. What matters is that I can see other people crafting their own thoughts and ideas about Sinclair's character and sharing those ideas with others which can provide new perspectives and layers to understanding and creating with the character. Or that's how I feel about things, at least.

Ignoring the dad part
I think she'd known by the way La Manchaland fell that it wouldn't have ended well for Don Quixote, especially since he chose to remain and seal them all away instead of doing away with his treacherous Kindreds. She long since made her peace with the fact that this would probably be the last time she ever saw him, and was just determined to carry out his final will and make sure that Sancho would be free of La Manchaland and be able to go wherever she wanted (or was fated) to go. Even if it meant staying in place for a while.
Sancho it feels like she figured out what her general path would be, so set things up to make it easier to find her way (including I'm assuming telling Vergilius her location.)
Their ultimate clash would've been a bittersweet ending, but one I think Bari would've seen as necessary to give the both of them closure they both desperately needed.

I think one of the fun aspects of 'opposites attract' ships is that, at their cores, they quite often end up being far more similar than they expect/would like to admit!
Sancho appears to be a pessimist bordering on nihilism because of her lonely past, wherein she had literally no one until Don Quixote swooped in and made her into his Kindred. But even when she had a family, the main pleasures she sought out were rooted in their connection to her sire. And she hides her true enthusiasm about things for various reasons, among them likely insecurity about being openly happy considering said past.
And if Meursault is anything like his literary counterpart, he may have also had a mother who he held a connection to and whose death affected him greatly. He seeks out simple pleasures because those are just what makes him happy. He's clearly not emotionless, just suppresses his own thoughts and ideas a lot because, as he says, most people don't really listen to him in full because when he Does talk, he has so much to say that it puts people off.
In the end, they both appear to be people who put up different facades, one of overzealotry and one of indifference, because they believe that their true feelings wouldn't really be understood by others.

Um, let's see. Some basic ones...
- Because of the way their head is, they can't really eat. And they really don't need to since the Golden Bough in their prosthetic head takes care of their body's needs and keeps them up and going. Though they could theoretically ingest something through a tube in their esophagus, they tend to find it unpleasant and so avoid it. But they will hold food when with others and let someone else eat it just to feel included.
- Because of the above reasons they don't really need to breathe also.
- Deal with some chronic/phantom pain issues due to all the rewinds. Especially if they've had to rewind the Sinners several times in a single day.
- The flames on their head react to the proximity of hands/other objects getting close and reduce if something comes too near. So they don't accidentally burn other people or objects by standing near them. But if you held your hands a certain distance away you'd feel the heat coming off of it. But if you're fast enough you could theoretically light something off of the flames. The flames are nonreactive to combustibles/accelerants like gasoline.