Pin'd pieces still protect?

Yes, pinned pieces still attack squares and protect pieces, even if pinned to a king.

Of course this applies only if the king is the one trying to capture an enemy piece which is defended by a pinned piece.

Replacing the king with other pieces would allow the piece to be captured safely.

Black to Move (Sorry for the late response)

 In this situation I figured the Black King should be able to take the White Rook, and Why not?

How can the White Bishop protect the Rook when its pinned to its own King? 

How can the White Bishop protect the Rook when its pinned to its own King?

Them's the rules. King can never step into the line of fire of any piece, regardless of whether it's pinned. Even if the white rook wasn't there, the black king still couldn't move to d6 because it'd be stepping into the bishop's line of fire. 

If black's king captured the rook, it would be captured next before black's rook could capture the white king. Therefore, capturing the rook is illegal.

I'm sorry I've heard this explanation many times and it's complete gibberish. Logically speaking, this is a special case and an exception to the rules just like every other such special case in chess.

This is probably the most clear example of how pins work (and how they don't) that you'll see. Black is checkmated.

I made this up, of course.