I'm no psychologist, but I am a high school teacher, so I do deal a little with this stuff.
From everything I've seen, Nick doesn't show any signs of schizophrenia.
He has some clear social anxiety issues, and very likely has a touch of oppositional defiant disorder.
But even these are not particularly sever. On the large stage, under the bright lights, these issues are magnified.
But people with severe anxiety disorders won't even talk in front of a group of three or four strangers, let alone speaking at a press conference, and certainly aren't going to show up to publicly perform or compete in front of a crowd, especially if failure is a real possibility.
And people with sever oppositional defiant disorder don't become expert level anything because they don't learn squat from teachers or coaches. In fact, most of them end up in jail.
The Diaz brothers have their issues, but those issues are far overblown, and the fact is they've dealt with them extremely well in life.
The likes of Jon Jones (clear narcissist) and Rampage Jackson (anti-social) and "War Machine" (psychopath) could learn a lot from the Diaz brothers about getting over themselves and getting their shit together.
(I'd throw Mayhem in, but I think his issues are legitimately beyond his control.)