In the first diagram, I agree with Dink Heckler, it looks good to start by simply improving your position on the kingside and asking White what to do. It's hard to land on any definite conclusions, but my guess would be that Black is winning.
I'm wondering how you went from the first to the second diagram, but once there, it's easier to calculate in detail than the first diagram. Following TN's plans, 1...Kf5 2.Kd6 Nf3 3.Ke7 Nxh2 4.Kf7 and White does get one of Black's pawns, but if Black keeps his h pawn, it will be very hard, if not impossible, to stop. So, 4...h5 5.Kxg7 Ng4! (5...h4 6.Ne3+ is troublesome) and although material is currently equal, White has a hard time stopping Black's remaining pawn.
Cheating a little by consulting tablebases confirms that the final position is indeed winning for Black. That said, it takes some time and requires accurate play.
However, my first impression in the diagram is that I would like to keep Black's king on e4 and, like in the first diagram, improve Black's position before undertaking something, e.g. 1...Ke4 2.Kd6 Nf3 3.Ke6 and now, instead of 3...Nxh2 4.f5, which looks annoying, Black plays 3...h5!
aiming simply to advance the h pawn before taking White's pawn(s). White's pieces are awkwardly placed, so it is hard for him to create counterplay.
Once I set up this position with a diagram, I realized White could try 4.h3 h4 5.Ne7, but apparently Black wins by 5...Ng1 6.Nf5 Nxh3 7.Nxh4 Nxf4+ and 8...g5, trapping White's knight!
So it seems to me that Black is winning in both diagrams.