bishop vs knight and pawn

White can't win. It's drawn.

Just about the only possible way would be using the knight protected by the king to block off the bishop's path, then advancing the pawn the next two squares, repeating the process for the next square to be crossed. But that plan takes time to execute and black still has a king to assist; also the bishop can move to g5 or h4 in a key moment to block the knight or foil the blocking plan.

If it were a rook pawn, white's chances for a win would be a bit better since the bishop can only block its advance from one side.

Completely impossible, the bishop has far too many squares from which it can guard g5. In fact, it's not even possible for Black to guard all five squares along the d8-h4 diagonal at once...the bishop just has to keep shuffling along that diagonal and White has no way to push it off (Black can use his king to make waiting moves).

EDIT: Hmmm, just realized maybe the board is flipped and the white pawn is moving down the board...but in that case 1. ...Bc7 is a trivial draw for Black too, with an even longer diagonal to work with.

EDIT MK II: Hmmm, interesting. Just noticed it's not entirely as simple as I thought...Black needs to get his king a little nearer to the pawn; because White has the idea of using his knight (guarded by his king) to block the bishop's access to the square in front of the pawn. To prevent this Black needs to use his king to guard the squares where the knight could block the bishop, or place his king in front of the pawn so he can exchange the bishop for the knight when it is blocked and still have a drawn king-vs-king-and-pawn situation. It seems that such an endgame is only drawn when the defending side's king is near enough to the pawn, or at least its queening square. Or maybe it's because in this case the bishop has limited space to work with on the other side of the pawn...in which case a rook pawn does seem to have better winning chances.

Well, I think there's a slight chance, if you somehow get the knight to f6 and the king to f5 you might win, but it's hard.

Not really, Black plunks his bishop on h4 and it's still drawn. (Though yes, Black has to watch out for that plan from White and move his bishop to h4 before the knight goes to f6.) White can't chase away the bishop on h4 and still guard his knight at the same time; so if he wants to chase away the bishop with Kh5 then he must first move away the knight and give the bishop access to d8 and e7 again, whereas if he wants to keep the knight on f6 then his king can't approach the bishop.