Who was Kristina Frye and what happened to her?
Kristina was another "psychic," like Jane used to be. She made the same mistake of insulting Red John on TV, and she paid the price. In terms of "where did she end up?" I don't think the show ever said explicitly. Probably, she wound up in a mental institution. I'm thinking she probably wouldn't have survived long on her own if she didn't get help, with the state she was in, but the show never actually tells us what happened in the end.
Was she a real Psychic?
No. There are no such things as psychics. Nothing in the show has ever suggested real psychic powers exist. Kristina was just frustratingly obtuse about refusing to admit that her "powers" weren't real.
What did Red John do to her?
Again, it isn't explicitly said what he did. He probably tortured her. He may have done some hypnotic suggestion stuff (although I'm not sure how legit that is either.)
Bottom line, he broke her mind and convinced her that she was already dead. Then he set her loose to show Jane what happens when people mess with him. (As though Jane didn't already know.)
(It's also possible that Kristina Frye was always part of Red John's cult, and everything she did with Jane was just to mess with him, on Red John's behalf. In that case, the thing about thinking she was already dead would have likely just been an act, and she ran off into the sunset afterwards, never to be seen or heard from again. That's just a side theory, though. The above answers are more likely, IMHO.)