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It's the worst case scenario for queens, of course. Just as you ask how to mate the solitary black king with the white king and a white rook in 2D chess. The mating method should always work.
If it doesn't always work, which means that there is a position from where the mate isn't possible ... then that number of queens isn't the answer we are looking for.
To answer the other question: there exists a checkmate with two queens. Just pin the king into a corner with one, and guard that queen with another.