Interesting Ending Knight + pawn vs Rook - main plans (white and black) From the feedback received I updated the main line (from pos 39). I post an update of this endgame. Now it is more clear that f7 is a weak point, and it is tricky for black to try to stop the two menaces: f7 and play on the c file ... It is not clear whether to try to take e5 pawn or play on the queenside without stopping rook menaces.

Edit 1: From your suggestions I tried to improve the game ... but somehow I think that white can improve the game ... I arrive at this position that seems nice for black (with idea of b3 and promote ...)

[Title "Side to move: Black"]
[StartFlipped "0"]
[fen "8/5p2/4p2p/3pP1pP/1p1n4/k7/P2R1KP1/8 b - - 5 45"]


Here I post the update the rest of analysis :

[Event "Android 2.3.5"]
[Site "GT-I9001"]
[Date "2015.04.20"]
[Round "-"]
[White "Stockfish 4"]
[Black "Mandor"]
[Result "*"]
[Startply "75"]
[fen ""]

1.e4 e6 2.d4 d5 3.Nc3 Nf6 4.e5 Nfd7 5.Nce2 c5 6.c3 Nc6 7.f4 Qb6 8.Nf3 cxd4 9.cxd4 Be7 10.Nc3 O-O 11.Be2 a6 12.O-O Qa7 13.Be3 b5 14.Qc2 Nb6 15.b3 b4 16.Nb5 Qd7 17.Nd6 Bxd6 18.exd6 Qxd6 19.Ne5 Ne7 20.Bd3 g6 21.Rac1 a5 22.Qc5 Qxc5 23.dxc5 Nd7 24.c6 Nxe5 25.fxe5 Ba6 26.Bxa6 Rxa6 27.Bc5 Nxc6 28.Bxf8 Kxf8 29.Rfe1 Ke7 30.Rc2 Kd7 31.Rf2 Nd8 32.Kf1 Rc6 33.Ke2 Rc2+ 34.Kf1 Rxf2+ 35.Kxf2 Nc6 36.h3 Kc7 37.h4 Kb6 38.Kf3 h6 39.Kg4 Kb5 40.Kg3 a4 41.bxa4+ Kxa4 42.h5 g5 43.Re2 Ka3 44.Kf2 Nd4 45.Rd2 b3 46.axb3 Nc6 47.Ke3 Kb4 48. Rc2 Kb5 49.Rc1 Nxe5 50.Rc7 Kb6 51.Re7 Kc6 52.b4 Kd6 53.Rb7 Ng4+ 54.Kd4 e5+ 55.Kc3 d4+ 56.Kc4 Ne3+ 57.Kd3 Nxg2 *


All suggestions are welcome! Thanks!

Edit 2:
From this position : 8/5p1p/1kn1p1p1/p2pP3/1p5P/1P3K2/P5P1/4R3 b - - 2 38

Summarizing until now from the core position. Is it possible to win with black? How? :)
1) Plan put Knight on f6 seems to fail due to: 38. Kf3 (for example) .. Nd4+ 39. Kf4 Nb5 40. Rf1! (and ok Knight, you can occupy f6 and I will let rook take f7 for example with Ke3 )

2) Plan to change e5 pawn for f7 pawn I did not manage to have anything. Usually the white rook could counter attack on the back rank, and somehow the king and rook will take the kingside pawns. 

3) Plan to put king on b5 for me seems the most promising... but I did not manage to make it work : 38. Kf3 (to be coherent) h6 39. Kg4 (yes seems strange) Kb5 40. Kf4 a4 (with initial idea but ..) 41. bxa4+ Kxa4 42. Rc1! .. and what to do? Kb5 ?¿ And how to progress ? :(  (I though something like 42. Rc1 42. g5 43. hxg5 hxg5 44. Kxg5 Nxe5 45. Kf6 ...

Other ideas?¿
First of all, I think white can only play to hold. The question is whether black can really create winning chances. 

All the h3-h4-Kf3-Kg4-Kg3 stuff in the game and your line, is pretty much just white doing nothing. 

Personally I would put the king on f4 straight away to free up the rook. And then put the rook on the c-file. This should limit blacks options by attacking the knight, cutting off the king and threatening a backrank invasion should the knight ever move.

In this scenario even playing a4 cannot easily be engineered because the black king wouldn't be able to take back on a4 and keep protecting the knight.

There are some other motifs in this position. When the white king reaches f4, black pretty much has to play h6 to prevent the invasion. And if black plays h6 white has to play h4, otherwise g5+ will always threaten to win the e5 pawn. If white starts with h4, I would seriously consider h6 with black because white might play h5 the next move, and suddenly the black kingside becomes pretty morose. (So, in the line you give 37.h4 Kb6 38. h5 might be an idea for white. 38…g5 39.h6 and the g5 pawn will fall, 38…h6 39.hxg6 fxg6 and at least there is another open file, although that one isn't so clear to me, but still, why give white the option?)  

[FEN ""]
[Startply "75"]
[Event "Android 2.3.5"]
[Site "GT-I9001"]
[Date "2015.04.20"]
[Round "-"]
[White "Stockfish 4"]
[Black "Mandor"]
[Result "*"]

1.e4 e6 2.d4 d5 3.Nc3 Nf6 4.e5 Nfd7 5.Nce2 c5 6.c3 Nc6 7.f4 Qb6 8.Nf3 cxd4
9.cxd4 Be7 10.Nc3 O-O 11.Be2 a6 12.O-O Qa7 13.Be3 b5 14.Qc2 Nb6 15.b3 b4 
16.Nb5 Qd7 17.Nd6 Bxd6 18.exd6 Qxd6 19.Ne5 Ne7 20.Bd3 g6 21.Rac1 a5 22.Qc5
Qxc5 23.dxc5 Nd7 24.c6 Nxe5 25.fxe5 Ba6 26.Bxa6 Rxa6 27.Bc5 Nxc6 28.Bxf8 
Kxf8 29.Rfe1 Ke7 30.Rc2 Kd7 31.Rf2 Nd8 32.Kf1 Rc6 33.Ke2 Rc2+ 
34.Kf1 Rxf2+ 35.Kxf2 Nc6 36.h4 Kc7 37.Kf3 Kb6 38.Kf4 h6 39.Rc1 


Now, black can still play for a win, by bringing the knight to c3. For example 39…Nd4 40.Rc8 Ne2+ 41.Ke3 Nc3 42.Rf8 this is extremely sharp and there are many options. White could go 39.Re2 first and the Rc2 and try to defend passively. Or maybe after 41…Nc3 he could just check the black king from behind and only go to f8 after the white kind went to the seven's …