Let's start with a simple one.
King and Pawn Endgame Puzzles
1...f6 2. exf6 in your third puzle is a draw.
Your second puzle has alternative moves and you missed a mate in one.
in your first puzzle shown with K and pawn if black K keeps to the same side
of white K it is a draw.

1...f6 2. exf6 in your third puzle is a draw.
Your second puzle has alternative moves and you missed a mate in one.
I fixed the second puzzle by changing it a bit, because the final mate is on g4 instead of g3. Also, I realized that 2.exf6 was a draw,(2...Kf7 3.g5 d4 4.Ke2 c3 5.Kd3 Ke6) but 2.h4 would have won(2...fxe5 3.fxe5 Ke7 4.h5) if it wasn't for 2...g5. Now if 4.exf6??, black has 4...gxh4. It turns out that 4.hxg5 draws,(4...fxe5 5.fxe5 d4 5.a4 Kf7 6.Kc2 Kg6 7.e6 Kg7), but as a reward for finding 2...g5, I wanted to add some life. Also, I know that I could have gone faster, but I decided to do a bit of Cat and Mouse.
If you find any good King and Pawn endgame puzzles, post them here. This is where you would put something like Reti's 1921 study.