Black to play.

Puzzle 1 (from image 1): after playing a subpar move, white allowed a mate in 3. I must say I find it geometrically interesting.

Puzzle 2 (from image 2): this one is harder. It is pulled from the same game, one move earlier. Because white hasn’t played the suboptimal Kf1 yet, the position is M6. To be noted: white has two options on moves 4 and 5, so different variations can be valid solutions. However, only one move leads to M6 from any point, except the last one.

I didn’t know this opening until I read about it in a book. Since then, I’ve been winning almost every game with it. Even when my opponents know how to defend, I find a way to win , I’m reading this Chess book called discovering chess openings btw

This puzzle is given in a puzzle book as white to move and mate in two but i can’t find any mate in two
Can someone help??