Two bishops and pawn vs bishop?

Is this usually won?

I am also interested, I would assume the two bishops is won. Does anyone know definitively?

That depends. Can you win a K+2B's vs. K position?

Yes, this is indeed a straightforward win. After all, the weaker side can't sac his bishop for the pawn since two bishops are enough to force mate against a lone king. That means he must try to blockade the pawn, but the stronger side will have a bishop of the same color that can guard the square in front of the pawn, so with the king also assisting the pawn's advance, there's just no hope for the defender. Trading bishops doesn't save the game, either, because K+B+P vs. K is also an easy forced win. 

The only exception I can think of offhand would be if the stronger side has a wrong-colored rook pawn; the defender may sometimes have drawing chances in this case. For instance:

In the position at left, Black can repeatedly play Bb2-Ba1-Bb2-Ba1, and if White brings his bishop onto the long diagonal, Black can safely exchange bishops due to the resulting endgame being drawn.

Yes.

http://www.youtube.com/watch?v=FvFLNvQ93bQ

http://www.youtube.com/watch?v=uimbIq9h_7A

http://www.youtube.com/watch?v=WhxmvaoNZns

http://www.youtube.com/watch?v=cA3c1ORODsw

http://www.youtube.com/watch?v=ZDGjiNxXDJ8

http://www.youtube.com/watch?v=Vqjik_DLXhA

To practice (When you refresh it gives you a new random position.):

http://www.chessvideos.tv/endgame-training/two-bishop-checkmate.php

two bishops + pawn vs two bishops will usually be drawn, since you can usually sac a bishop for the pawn and have a draw. There are going to be some exceptional positions where the pieces are awkardly placed, but they are rare. A pawn plus in a two bishop ending, though, I don't know if that's decisive or not (eg 4 pawns vs 3 pawns). In a one bishop ending, it is usually enough to win.

If all the pawns are on one side, then the only piece for which an extra pawn suffices to win is the queen. For all the others, the weaker side can set up a solid entrenchment where the only way to progress for the stronger side is to keep trading pawns, but eventually there will be only one pawn standing, which the weaker side's king can blockade for an easy draw.

Two bishops and a pawn vs two bishops should be a draw.  To me there doesn't seem to be a way to oust the king away from the critical squares with his other bishop undermining any potential zugzwang positions and, at the same time, creating other threats, such as picking off the pawn in support with the king and so on.

Does white win?

Yes.  See my post with your position.

Correct! I made up the position and thought it was a draw because white should not exchange bishops on the long diagonal. But Stockfish made me see the error of my ways.

What about a seventh-rank pawn with the opponents bishop blockading and the opponents king cut off by the pair of bishops?

Post a diagram?