Hello! First off, thank you so much!! ❤ And thank you for the ask as well! I've had this sitting in my askbox for a while but I'm a shy little baby so I'm only now answering it! Sorry about that!
Ahhh, headcanons. I had to think about this for a bit. Definitely hc them both as gay. Just two very gay dudes to me!
I LOVE trans Reigen. I don't hc him as trans, but I see it and I get it!! (Now that I stop to think about it, all of my favorite fics feature trans Reigen, actually.) It makes a lot of sense, especially with all the queer-coding that exists around his character!
As far as them getting together goes: I think for Reigen, it may have been love at first sight, but I don't see him being emotionally put together enough at that moment in time to fully register it, or even pay attention to it. He would probably do his best to suppress it for as long as he's able. Needless to say, I do not see him being the one to confess lol.
On Serizawa's side, I think it would a gradual realization over the course of a year or so. As much as I want them to make-out sloppy right away, it doesn't make sense for either of them. They're both way too emotionally stunted and def need time figuring their own crap out before they can pursue a relationship with each other.
All this to say, I think they'd have an agonizingly long, very drawn out slow-burn relationship lol.
Oh! And as far as big spoon/little spoon goes, I think they switch back and forth :')