a4 is probably the only move for his Q, since your treat of Qg4 is somewhat neutralized.

He should be looking to exchange pieces now though since he's got a 4-2 pawn majority on the Q-side.

While your Q-side pawns are weak, trying to pick them off while all the heavy pieces are still around shouldn't be a priority imo. Sure take them if you safely can, but better to simplify and get to the endgame.

Mating threats like Qd4 are kinda pointless, with your two rooks on your back rank and since Rd1 just ends the threat right there.