Second challenge: find the fastest position where white/black to move is mate, but the queens never move and the queens are not the mating pieces.
A queen (or any piece) can never be a mating piece unless it moves anyway. Read this thread (all posts ): https://www.chess.com/forum/view/endgames/how-can-you-deliver-checkmate-with-a-king
It is possible though to specify that the queen does not attack the king in the checkmate position.
My attempt.