But here's the real wrench in that idea, if Sana were a guy, trans doesn't even come into the equation, wouldn't she have been drafted into the space war like every other able male? There's a reason no male students exist on screen and that is it, after all, they were all drafted from what I remember and the only reason Sensei wasn't was because he's a teacher (don't ask me how sending students and not teachers makes any sense whatsoever, it actually does make sense in the 'typical government move' kind of way, meaning it makes sense that they would do this even if doing it makes no sense). This is a time of war with an apparent draft, so a male is a male, trans or not, they don't have time to mess around trying to determine gender classification for the draft outside of obvious cases.
Yes, I'm pretty sure we would as I'm not sure how much we can divulge of the cards without getting in trouble, all I know is we can't share them. Considering how guarded they are now, I'm certainly not taking the risk by saying whether Sana has one or not.
It's an all girls school at the moment because of the space war.
But that again comes to the idea that she wouldn't out Sana, something there or not. For all we know, she could only be telling us that to hide Sana.