The reason bishops are sacrificed is that they are the least likely to be stopped from being sacrificed, compared to a knight or a pawn for whom the a6 / h6 takes 4 moves. The bishop sacrifice is usually not stopped from a direct threat to the king (except for the French Defence),
Another reason: a bishop sacrifice opens up the opponent's king more. Also ...
After 7.Bd2 Black has three options:
Black can pull the dark bishop back. Retreating to c5 doesn't work, since White can just push the b pawn forward, and force the dark bishop to retreat again, so you'd have to go back to d6 or further. The issue with this is tempo - you've giving white a free turn to develop.
You can try to ...
There isn't a sacrifice in the line you gave. I assume you man 6...Bb4+.
The bishop is a bad bishop because it's blocked by its own pawns in the center. 7.Bd2 is virtually forced trading black's bad bishop for white's good bishop. The alternatives for white just aren't very good.
It also frees up black's position because he can play d6 to develop the other ...
That is not a sacrifice at all. It is an exchange. You get rid of a bad bishop for his better one. It is positional play for a very minor advantage. But still an advantage. Enough small ones add up to be enough to win material and the game.
Mostly when the engine suggests a such exchange maneuverer it means that either your piece has no future, or the blocking piece has a very good future. Since you need to move the bishop somewhere to get castled, it chooses to exchange it off.
If you look for plans in the variation you given, the most natural way for White to proceed is to break in the center ...
Once white has put pawns on the central white squares of d3, c4 and e4 his white squared bishop becomes very bad, because its mobility is drastically reduced, and his dark squared bishop becomes essential for protecting the dark squares that have become weak thanks to the pawn moves.
That means that 7.Bd2 is a blunder because it allows black to exchange the ...
I wouldn't say it was a "sacrifice", it was more like an exchange of bishops.
My lichess engine was actually giving me ...Bd6 as the first move.
I don't understand why it wants me to move my bishop to b4 in the first place
Me neither. I doubt anyone here will have an idea. Stockfish doesn't tell us why. If I have to make a guess, I would say the ...
Not worth it.
Tactic used by low rated players which might work against other low rated players but would fail to a halfway decent player.
Run the position through an engine of your choice and see what it says.
No official name but patzer fish rookie beginner could work.
Can not comment.
@David Bateman: If those ratings are online then they are barely ...