Why is Bd6 better than Be7, Bc5 and Bb4?

1. when the pawns are on c6 and d5 that means that your dark bishop is your best bishop
2. after c6 and d5 the dark square around them are weak and the bishop takes control of those square.
3. the bishop on e7 is not controling alot of square on c5 and b4 it can get kicked around with a3 b4 or Na4. I am 2100 take that into account.

Bd6 has two big advantages that haven't been mentioned. The first is that it protects the b8 square for your rook. Your rook naturally belongs on the half-open file, and White really wants to play Bf4 to keep you from doing that. (You can put your bishop on d6 later if that happens, but you've wasted a tempo and exchanging bishops makes it easier for the white knight to establish itself at c5.) The second is that, later in the game, e5 will likely be a very powerful square for the bishop. (Or sooner, if White tries Bg5.)

Bd6 is the most active square. No, there's not an immediate threat but it does attack h2 which could turn into something later.

Be7 is too passive. It's not smart to "protect against pins" that haven't even happened yet. There's lots of unpin combinations that actually lead to the pinning side being worse. Also, white can't really capitalize on a pin since the knight can't come to e4 or d5. Lastly, the bishop on e7 blocks the open e-file which could turn into a strong attack if white doesn't castle quickly.

Bc5 isn't that bad but after white castles the bishop isn't doing much.

Bb4 doesn't do much either. Normally you would play Bb4 to control the e4 square but white isn't threatening anything there. You could double the c-pawns but that doesn't really do anything. White will just play c4 at some point and end up with a slightly better position because of the 2 bishops.

e7 is a very passive square for the bishop. Since White is expected to castle on the kingside, there is no reason not to prefer ...Bd6 over ...Be7. The pin on the f6 knight is not too much of a problem precisely because a ..Bc7, ..Qd6 continuation is always on the table.

...Bb4 has a similar problem as ...Be7 because after 0-0 the bishop is doing nothing on b4 (exchanging it for the knight would not be a great idea)

This leaves us with the options ...Bd6 and ...Bc5. I don't have a clear idea of which one is better but ...Bd6 seems more natural to me for an attack on h2. I guess ...Bd6 allows Black to push the central pawns if needed, but leaving them on c6 and d5 is probably best. I don't think the pin on the f2 pawn is that relevant as White will probably never try to play f4 in this position. Anyway I wouldn't say ...Bc5 is an inferior move.