Was Gabriel Osbourne really a psychic?

Gabriel Osbourne is not a psychic. As Patrick Jane himself would say: "There's no such things as psychics."

It's possible that Gabriel was mentally unstable to the point that he actually believed he was psychic himself (the fact that his sister - a close personal support in his life - also promoted him as psychic surely didn't help.) He was certainly a little bit "off." That said, nothing presented in the course of the show has ever suggested that there are any REAL supernatural powers out there, so there's no reason to start thinking so on account of Gabriel.

As for how Gabriel could have known what he knew; Lisbon suggested two possibilities herself:

1) he might have a friend in the evidence lab (or other menial position in law enforcement.)

2) he might be the killer (this one is later proven false, of course.)

On top of that, there was an earlier episode (S04E03: "Pretty Red Balloon") where Jane himself did the whole "psychically predict where the victim is in the middle of the woods" gag, and he even stopped to explain how he did it. IIRC, Jane talked about how "saying it's near a body of water is a safe guess" because there's almost always a pond or a stream or something in the woods.

Gabriel is an established psychic, for better or for worse, and he probably knows all the same tricks Jane does. How to be just specific enough to get people going while staying vague enough to avoid outing himself. It's what the show is all about.

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.