The show make it quite obvious he is not a psychic. After all when it really matters (saving not only his life, but his sister's), he failed to deliver. As french joke says : "If I call a psychic and she ask my name, I immediatly hang up".
About the predictions :
1) The main one with the bodies : the most obvious would be that he saw one of the murders/dumping.
The dumping ground was not far (less than on mile) from the 'making out location', it would make sense that he stalk this place in order to get information about current relationships, in order to get credit as a psychic (As a bonus point, it also explain how he knew for his neighbourgh's boyfriend).
I know I am reaching. But does it really seems so farfetched ? That's hot reading 101.
It also answers the question about if he really believe being a psychic. If he did hot reading, it's that he knew he was a fraud.
2) Wyllie state of mind/ Vega death/location of the shooting :
The first cold reading was quite limited. Just that Wyllie is very sad. And Wyllie confirmed it, it was basically written on the face of Wyllie.
The he/she was a 10/90 Gambit.
A guy tends to be more sad about a girlfriend/mother (without going into cliché, I would assume a mentalist should spot a gay/bi/other a mile away, at least in a TV show).
Additionnaly, Gabriel had time to do research. He knew Vega was the only recent death in Wyllie life (same for other members of the team), and her death must have been public enough so it would be easy to find where she was shot.
Then Wyllie himself confirmed it was Michelle (not Vega, Michelle). It's a mix of cold and hot reading. Jane did way better along the show.
3) Murder will occurs the next day : this one was a self-fulfilling prophecy. by taunting the murderer, he ensure he will act quickly or look weak/afraid. And the best part of it, if it does not work, he can affirm that he prevented the murder by his intervention.