yes it depends on the situation

great exercise, i also made one where it's better to promote to a knight

I wonder whether there could be a situation where a player lost a game by promoting to Q, which he could have won by promoting to R or B.

I don't think so, but sometimes promoting to a R or a B does not result in stalemate but nevertheless leads to a winning position, and promoting to a Q results in stalemae. See the topic I posted in the forum Endgame Study for examples.

How do you underpromote on chess.com? Every time I promote, a Queen automatically comes on the board?