If I had my Queen taken by the opponent and the opponent promotes his pawn - are they allowed to promote it to a Queen using my Queen as the one they promote to, even if they still have their Queen? Such that they would have two Queens in their control?
yes, he can have two queens or more.
When your opponent promotes his pawns on the eighth rank it doesn't matter if your queen has been captured or not. This has nothing to do with pawn promotion.
The player can choose to promote his pawn to a queen, knight, bishop or rook of the same color by replacing the pawn on the same square in one move.
He is not limited to pieces that have already been taken off the board, but he can take chess pieces from other chess sets if they are required or use other items.
For example, if a queen is not available he can put a rook upside down on to the square and claim it to be a queen. Or he can put a stone on the square and say: "This is a queen!"
He, theoretically, can promote all his eight pawns to queens, which means that there would be eight queens on the board.
But this never happens, you usually resign the game when the opponent promotes a pawn to a queen and if he would be a queen up because in this case he would have an overwhelming material advantage and you would lose the game for sure.