Bullet chess can make you better but only when played with regular, slow chess too. If you only play bullet chess, you will get better at bullet only. You could lose the ability to put deep thought into the ordinary chess game and if you encounter a pattern on the board that you don’t recognize, you will be floundering. Bullet chess can be great for practicing time-poor end games.
Yes more than one pawn can be promoted in chess. Not only can pawns of each color in a game of chess be promoted, but more than one pawn of a single color may be promoted too. All that is required for a pawn to be promoted is for it to make it onto the final rank of the board, there are no other constraints. However, once a pawn makes it to that rank it must be promoted immediately.