The correct moves are:

Mate in two (326)

1. Qf2 Kh1 or Kh3
2. Qh2, and checkmate!

Mate in two (346)

1. Qe3 Kd1
2. Qd2, and checkmate!

or

1. Qe3 Kf1
2. Bd2, and checkmate!