Black queen takes the knight on C3, putting white in check while threatening the rook. With the bishop on A4 and the knight on D4, the white king can only move to F1/2. Blocking with the bishop is ineffective since then the queen will just take the rook to maintain check.
When the king is moved (regardless if F1 or 2), the black knight moves to H7, opening the column for check through the rook, while threatening the queen. Queen can’t block on F4 (unprotected), so the white king has to make a run for it or use the knight to block, white queen is gone, white rook and bishop still threatened through the black queen.
Very good! Blocking with bd2 actually allows you to extend this to a mate in 12 but as you mentioned it’s easy to see after Qxa1. Stockfish gives the initial position #9 which follows pretty much exactly as you stated. The only reason it’s 9 is because white can extend by either sacrificing the queen on g7 or giving a pawn check on h7. After the f file is open white is simply throwing all their pieces in the way to extend the mate.
This position is mate in 9 for black. There are a lot of variations on how it ends but after Qxc3+, it’s basically game over. There are several different ways to defend so put it in an analysis board and see how many ways you can find.
knight on d4 to f5.
relax, it looks like black can pull it off in maybe 5 or 6 more moves.
blacks queen to take white knight for check to take rook then set up mate with supporting bishop.
black knight to E8 to cover pawn on G7 maybe?
I’m gonna say knight to h5 but I am admittedly bad at this.
