Chess Puzzle from French Team Top 12 Championships

From the current French Team Top 12 Championship happening in Belfort,

#1
Round 6 game  between GM Etienne Bacrot (2695) - GM Dmitry Svetushkin (2597), White has just played 45  Qf4-d6. What would you play as Black? Do you see any threats?



* In the game, Black queened the d-pawn (45...d2-d1=Q) but this allowed a petite combinaison: 46.Ng6+ Kg8 47.Qxb8+ Kh7 48.Ne7.
Stockfish recommends 45...Kf8-e8 which is still difficult for Black but not losing immediately.

#2
This is not so much a puzzle as it is puzzling. Round 6 between IM Jean-Rene Koch (2484) - GM Kamil Miton (2622), White has just played 53 Bd1xh5. What would you play as Black? (scroll down to ** and highlight to reveal the answer, that is, after you have a think, if you are interested to know what happened.)





**To maintain the draw, you would expect Black to capture b3 with the Knight, ie 53...Nc5xb3 but no, the game record shows 53...Nc5xa4. Stockfish on iPad thinks this is a +73 White advantage but the second puzzling thing occurred: the game was drawn. I can only surmise that both players were in time trouble? OR possible but unlikely: the game score is corrupted?
Now here is the puzzle: Can you win as White from 53...Nc5xa4? (see below *** and highlight to reveal the answer)
(the full game score:
IM Koch, Jean-Rene (2484) - GM Miton, Kamil (2622)
TCh-FRA Top 12 2012 Belfort FRA (6.4), 2012.06.05
1.e4 c5 2.Nf3 Nc6 3.d4 cxd4 4.Nxd4 e5 5.Nb5 d6 6.c4 Be7 7.N1c3 a6 8.Na3 Nf6 9.Nc2 O-O 10.Bd3 Bg4 11.f3 Be6 12.Be3 Nh5 13.Nd5 Bg5 14.Bb6 Qd7 15.O-O Ne7 16.a4 Rac8 17.Nxe7+ Qxe7 18.b3 g6 19.Nb4 Bf4 20.g3 Qg5 21.Ra2 a5 22.Nd5 Bxd5 23.exd5 Be3+ 24.Bxe3 Qxe3+ 25.Kh1 f5 26.Re2 Qc5 27.Bc2 Nf6 28.Qd2 Qc7 29.Kg2 Nd7 30.Rfe1 Nc5 31.f4 e4 32.Qd4 Qg7 33.Qxg7+ Kxg7 34.Kf2 h6 35.Ke3 Kf6 36.Rf1 Rce8 37.Ref2 Re7 38.h3 Kg7 39.Rg2 Ref7 40.g4 fxg4 41.Rxg4 g5 42.h4 Rxf4 43.Rfxf4 Rxf4 44.Rxf4 gxf4+ 45.Kxf4 Kg6 46.Bxe4+ Kh5 47.Bc2 Kxh4 48.Bd1 Kh3 49.Kf5 Kg3 50.Kf6 Kf4 51.Ke7 Ke5 52.Kd8 h5 53.Bxh5 Nxa4 54.bxa4 Kd4 55.Kc7 Ke5 56.Kb6 Kf6 57.Kxa5 Ke7 58.Kb6 Kd8 59.a5 Kc8 60.Be8 Kb8 61.Bb5 Kc8 62.Be8 Kb8 63.Bb5 ½-½)
***At move 58...Ke7-d8, Stockfish announces mate in 22 with 59 Kb6xb7.
At move 59...Kd8-c8, Stockfish announces mate in 17 with 60 Bh5-g4+.
At move 60...Kc8-b8, Stockfish announces mate in 6 with 61 Be8-d7.


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