As simple as ever. Find the best move/line for White to continue with. Quick! Before anyone does it!

resign???

I originally said Qh8+, but that doesn't work because the White King can still move to c4.

Well, first of all, a thousand sincere apologies. It was an error. I had spotted it immediately after posting it, but due to some reason, I had to leave the laptop idle. Anyways, it is clear but you can give the answer. I'll post another one soon. 

Another one, again simple. 

Qh8+ Kf7

Qg7+ Kxf7 (only legal move)

Stalemate

1.Qh5+ Ke7 2.Qf7#

on the second puzzle..... Bb5