hmmmm i have a lot of very small and insignificant headcanons about very specific things so being asked such a broad question is really hard to answer but ill try!
tsukasa- stress baker, has a complex relationship with his gender and sexuality (a lot of internalized things in that head of his lol), has a very strict sleeping schedule and is out like a light by 11pm max (usually earlier tho), speaking of he will sometimes set an alarm for 2am to call nene(and rui sometimes) and make them go to sleep, he spoils wxs and buys them their fav sweets and little trinkets that remind him of them
emu- rich girl that has a private chef so everytime she visits someones house and eats a home cooked meal she feels strange warmth in her chest, transgender girl (i love neopronouns emu but idt neoprns work in japanese), names all of her plushies, she is not stupid but there's some "common sense" or "basic knowledge" things she struggles with due to being a neglected girl in a misogynistic rich family
nene- she is a fortnite player bc i am too and i love to project on my favs, she has online friends and is severly chronically online (or at least used to be), bites her nails when she's nervous, on certain days she dresses like a teenage boy and on the others she embraces her femininity and dresses like a really cute girl, additionally i also really like...the idea of nene doing girly things because i think the tomboy nene is such a popular hc that the girly girl nene just makes me happy (she is genderfluid to me tho)
rui- he will get fixated on a task and forget to eat, drink, sleep until someone yells at him or he passes out, has low iron so everytime he stands up he has to quickly grab onto something or he will fall and hit himself, has gastritis and tummy issues but does nothing about it, his gender is a mystery and his sexuality is fruity in one way or the other, loves teasing tsukasa by drawing dicks in his notebook (tsukasa scolds him for it and calls him a perv but rui only does it for the reactions), tries the games nene recommends but is really ass at them and only really playes them to make her happy!

well considering we got nene playing a guy in power of regret i dont think its impossible or out of reach idea but i doubt it would be for a big and important performance that the event focuses on. maybe for a practice or some sort of study :o although id really like for this to happen plsplsplsplsplsplspls ive been dreaming about tsukasa playing a female role for almost three years now.
i dont think a role of the opposite gender would bother tsukasa as we can see from the recent 4koma! it reminds me of the holy night event where he was a little taken aback "are you going to have me playing a little girl!?" but i think tsukasa has grown since and has come to terms with the fact he wont always be playing prince charming ^_^ so i dont think he would be against it, on the contrary i think it would be motivating for him to try something new!

ruikasa - sorcevalier (cliche) but i also love my alchemist x chef au
nenekasa - wl1 kasa (king) and knight nene. its an au that i really like where tsukasa is a king and nene is his personal knight and they have a really confusing codependant and avoidant relationship
emurui - i love my oomf mari's roselily au which is wedding emu and dark lily rui! doomed lovers
ruinene - tsks5 samurai set ruinene is so peak to me because i like the idea of nene coming from a powerful clan or a family and rui works for her as her guardian/right hand man and is ready to kill for her. "was i goo :3" looks at her with his eyes sparkling, body covered in blood (not his!!!)
emukasa - hmmm im not too sure bc i havent been thinking abt emukasa too much lately but i really like halloween emu x jester tsukasa. a fucked up duo. i will think more ^_^
emunene - knight emunene yuri everyone cheer 🤤 also...cliche but traveler x witch is so good its peak emunene to me.
polysho - either my jester au or my detective au :3 i can talk abt them a bit more if ur interested