The 69 position, could you do it?

Give two chess puzzles in the photo.

- In the first puzzle (yellow, left), White just killed a Black piece and now is turn of Black. Before death, victim had performed 69 moves (each capture is also a move).

- In the second puzzle (blue, right), only one Pawn is promoted, only 5 Black pieces were killed. A1 is concealed .Whose turn is unclear now.

a) Prove that White can “always” checkmate Black within 6 moves in the 1st puzzle, and within 9 moves in the 2nd puzzle.

b) Only consider 1st puzzle. Know the 5 following:

- No piece was killed in row 4. There are not "exactly" 2 pieces, which were killed in the same row. (However, more than 3 pieces is possible)

- There is a killer, who is dead now. At his 60th move and 90th move, he killed 2 White pieces.

- 2 bN were killed side by side (maybe adjacent in a row or a column or a diagonal), but none of them dead on the same row with bQ.  Before death, both bN had never stood at D8 or E8.

- The piece, who killed bQ is still alive.

- 2 pieces, who killed bB, move 6m+9 times and 6n-9 times (m counts the move of wP-A2, n counts the move of wP-D2, at the present).  Know that 1 of 2 killer above is standing next to only 1 other piece.

Please tell me exactly: which piece is the killer, and which piece is his victim (with their name and original location), where is the killer now?

For example: wP-B2 x bN-G8 at A4, killer is at A5. Or bQ x wP-F2 at F6, killer is dead...

https://www.dropbox.com/s/y4o2qx9z7fctm3d/69%20chess.jpg?dl=1