WARNINGS. He might have some inner monologue that hints at suicidal ideation from time to time, but he's not keen to talk about it. Generally I don't think there's anything about his character or his dialogue that would require a warning.
MEDICAL INFO. He sleeps a lot and eats a lot, moreso when he's upset. Otherwise he's a normal human.
MENTAL INFO. Minato used to house Death in his mind, and also he likes to repress everything that upsets him, so his mind's kinda a funny place. Aside from the fact that his Persona "live" there, too, depending on how you interpret it. I love mind reading but if things head in that direction, you'll probably need a primer on his situation, and it's quite complicated. xD; I'd be happy to plot something out with it, though!
FOURTH-WALLING. You're free to realize he sounds suspiciously like a video game protagonist, but as far as knowing P3 specifically, I'll have to go with no. He already has enough existential crises.
PHYSICAL CONTACT. Go right ahead. He won't mind.
ROMANCE/SEXUAL RELATIONS. Minato tends not to initiate things here, but he will likely go along with whatever someone else wants. He's more comfortable with ladies but he wouldn't say no to anyone male. OOCly, I'm totally open to anything. I will note that he'll be a hard sell on the concept of monogamy.
INJURE/KILL. He is most definitely a fighting oriented character, but he has very strong self-healing capabilities and is both post-canon and the protagonist. Basically, he's kind of godmodey. It is possible to kill him-- and very possible to injure him-- but he probably won't stay that way. Even moreso, he likes to fight as a team, and has absolutely no problem bringing backup to a fight. So while I'm happy to plot this out, you might want to be cautious about starting something with him unless your character has a specific plan on how to handle it.
DEVICE HACKING. This is fine. He's decent with technology but he doesn't know any hacking at all, so you're likely to manage without any problem if you're subtle.
THREADJACKING. I love threadjacking! Go right ahead.
BACKTAGGING. I also love backtagging. This is fine.