Bf4+
Qf3
wfb
Kh1
your queen can't be in contact with my king as you will also be in check
Leaving your queen in check is not legal, so Qh2 is not legal. Just like you can't put your own king next to the opponents king to checkmate.
If Kg2/1 then Bg4
Kg2, Bg4+
Qxg4
what's our score?
2.5-1.5 I lead
rematch?