Is it possible for someone to give me fake or stolen bitcoins?
How long do I wait to make sure a BTC is "legit" and truly mine?
The closest known way is to double spend bitcoins.
As far as stolen bitcoins, you will almost certainly touch them.
With Mt.Gox having stole so many and the silkroad bust having stole many, LOTS of stolen bitcoins.
It would be wise to wait for at least one confirmation.