M/A 1 is easy to guess: if f5 is possible then f6 is also possible, so by
the conventions of retrograde analysis the answer must be f6. Proving that
the pawn cannot be on f5 is harder, and I almost wrote to you that the
position is impossible.

The White bishop cannot have started at f1, and must therefore be the
result of an underpromotion. Since there had to be a path to the corner,
the pawn on b3 must have started at b2 and advanced after the bishop moved
to the corner. It follows that the other advanced White pawns started on d2
& f2, so the underpromoted pawn started at a2. Since the exits from a8 & c8
are blocked, the promotion must have happened at e8 or g8. To bypass
Black's KP, the pawn must have made 6 captures. These cannot include
Black's QB (which obviously never moved) or the KB (which stayed on black
squares) or Black's KKtP (which could at most move diagonally toward a1).
That leaves 7 pieces that the White pawn could capture:

a) The Black queen;
b) Both Black knights;
c) Black's KBP, or whatever it was promoted to;
d) A Black rook;
e) Whatever the Black KKtP was promoted to;
f) Another Black rook, but only if a Black pawn was promoted to a rook and
moved to a8.

Thus the KKtP must have been promoted. (Promoting the KBP doesn't increase
the number of captures available to the White pawn.) Passing through d2 or
f2 would force the White king to move, so it must have reached b2, making 5
captures. Since White's KB never moved, the Black pawn must have captured
all the other missing White pieces. Moreover, White's QKtP had to move to
b3 before the Black pawn could be promoted, so the White bishop was already
in the corner, and we can rule out (e). Thus Black promoted a pawn to a
rook on b1, but no White piece was available to interpose. (The QR has not
moved, and capturing the new Black rook would not allow it to reach a8.)
Thus the check was blocked by a Black piece, which can only be the KB.
Later the KB was captured by a White pawn, but there is only one pawn
capture unaccounted for. Thus the pawn on the KB file must have advanced
without capturing, and the pawn on e4 must have started at d2 and captured
the bishop on e3.

Finally, we come to the mystery pawn. Since it hasn't captured anything, it
must have advanced at least to f4 before White's KR could throw itself in
front of Black's KKtP. After b1=R by Black, most White pieces were already
in the positions shown. The bishop could not move except to capture the
Black rook, and the QP had to wait on d2 to capture the Black bishop.
White's only move is thus to push the KBP. The Black pieces had to leave
the corner, but a bishop move would have discovered check and there was
still a pawn on d2, so there must have been a sequence like
1. ...   Rb2
2. Bb1 Ra2
(The Black king & White bishop could dance when the rook is on b2, but the
result is the same.) Once again, White's only move is a push, so the pawn
must be on f6. As shown below, the position is possible.

 1. Nc3      Nf6
 2. Nd5      Ne4
 3. Nb6      Ng3
 4. Nxc8     Nxf1
 5. Nb6      Ng3
 6. Nd5      Ne4
 7. Nf6+     gxf6
 8. Nf3      Bh6
 9. Ne5      Be3
10. Rf1      Bc5
11. f4       Bb4
12. Rf3      Nc5
13. Rd3      Nb3
14. axb3     Nc6
15. Rd4      Na5
16. Re4      Nc4
17. bxc4     Kf8
18. Re3      Kg7
19. Rg3+     Kh6
20. Rd3      Rg8
21. Rd4      fxe5
22. Re4      Rg6
23. Re3      Rd6
24. Re4      Rd5
25. cxd5     Qh8
26. Re3      Qf6
27. Rd3      Qe6
28. dxe6     a6
29. dxf7     Rg8
30. fxg8=B   c6
31. Ba2      Kg7
32. b3       Bc5
33. Bb2      Ba3
34. Bd4      exd4
35. Rc3      dxc3
36. Qc1      Bb4
37. Qa3      Bc5
38. Qa5      Ba3
39. Bb1      Bc1
40. Qa3      Kg8
41. Qb2      cxb2
42. Ba2      b1=R
43. f5       Rb2
44. Bb1      Ra2
45. f6       Ra5
46. Ba2      Rg5
47. Bb1      Kh8
48. Ba2      Rg8
49. Bb1      Bb2
50. Ba2      Bd4
51. Bb1      Be3
52. dxe3     Ra8
53. Ba2      Kg8
54. Bb1      Kf8
55. e4

Now 55. ... Ke8 56. Ba2 gives the position in the problem with Black to move.
55. ... Kf7  56. Ba2 Ke8 gives the same position with White to move.