a) 1...Qd6+, 2. Kg1+! (discovered check) Kg4, 3. Qf3#
b) 1...Qxe4, 2. Kg3+ (discovered check) Qh4+, 3. Rxh4+ winning the Black Queen and White wins
1.Rh1 looks really good to my eye- it helps defang the check from d6 in some lines I can imagine, and it also indirectly protects the e4 pawn where Kg3 gives a deadly discovered check. I tried to make 1.g4+ work, but the naked white king was a problem I can't see an out for.