Can a pawn be promoted to queen if the player is missing a knight, bishop or rook?
You can promote a pawn to any piece (other than a Pawn or King), regardless of how many of that piece is on the board. In theory, you could have nine Queens by the end of the game (unlikely, of course). 

Piece availability is not a concern, either. An upside-down rook (if available) is the recommended stand-in for a queen, though you may have to improvise due to limited resources (stacked checkers tiles also work well).