Yes you can promote to any piece but anything other than a queen is rare. I believe promoting to a Bishop is considered the rarest move in chess. 2 bishops of the same colour is legal. There's a good RYBKA vs Hikaru Nakamura game where this happens. That said its a long game 250+ moves. so not something to put in here.
As to why its legal... FIDE rules; not exactly the easiest read though; Source : https://www.fide.com/fide/handbook.html?id=171&view=article
I found some puzzle examples
Example 1: Queen Promotion - Result Stalemate
8[FEN "8/8/5b2/8/K7/4N3/kp6/8 w - - 0 1"]
1. Nd1 b1=Q 2. Nc3+ Bxc3 *
Example 2: Bishop Promotion - Black Wins (after about 50 moves of end game pain)
8[FEN "8/8/5b2/8/K7/4N3/kp6/8 w - - 0 1"]
1. Nd1 b1=B 2. Nc3+ Bxc3