Gender: I think if she did have gender wobbles it'd take a while to untangle them from 'do I actually dislike my assigned gender or is this residual General Self-Loathing?'
(That's a decently big 'if,' which is why I have a fic where they're amicable exes - they saw the problem coming and stopped dating while they were still friends.)
NOTP: Yusuke. ...If he's paying attention to her moods at all, he twigs quickly. But it's about 50/50 whether he is or not, and that does not a solid relationship make.
Random headcanon: I've noticed before that one of the voices in her hallucinations sounds like Sojiro. Notably, it's the 'why don't you SAY SOMETHING' one... and that could be him.
(Re: gender, I can see Futaba landing where I am - 'if I do it, it's a thing girls do, you're all thinking about the social aspect of this way too hard.')