In both positions, it is white to move! How should white proceed in both?
I could be wrong, but in the first diagram, Rxf6 may win for white, because of Rxf6 Bxf6 Qg4+ (Bg7?? Bh6 and Black is defenseless) Kh8 Rf1 followed by Bh6.
If Rxf6 dxc3, then we just play Qg4+ Kh8 Bh6 Bxf6 then Rf1 with the same idea as the previous variation.
(1) I looked at Ne4 for a while, but it just seems to be meh. The problem is that the Q is stuck defending g2. Looking around for a better way to guard that square led me to 1. Rf3. Now 1...dc 2. Rg3+ Kh1 3. B:c3 threatens B:f6 freeing h5 for the Q. This has to be best.
Of course Black can play other than 1...dc. But Rg3 and Ne4 are still good moves for white, putting two pieces on very active squares and building an attack while at the same time defusing Black's attack.
R. Praggnanandhaa made a crucial mistake of 1. Ke3??? (losing move). Correct move is 1. Ke2! leading to a draw.
The second puzzle is a really nice one- it took me a couple of minutes to figure out what was special about the position- I guessed the right first move, but for the wrong reason- I was worried about the bishop checking the king for a tempo, but that wasn't the problem with 1.Ke3?? I don't think I have seen that motif before.