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About the last position:
Isn't quite easy for white to win. What if first white move his rook to a8. Black moves his king back and forward between h8 and h7. Meanwhile white moves his king to d7. Afterwards he sacrifices his rook for the bishop. white can force black away from the f7-pawn. White should be ware of stalemate but he wins if plays careful I am convinced.
contains my 2005-03-08 Comment, where I amused myself by devising a complete (legal) game of shatranj ending in a 'BLOCKADE STALEMATE IN 20 MOVES'. There is really no need to go to such lengths in this discussion of possible checkmates in a K + N versus K + B ending. My 2005-11-14 Comment demonstrates a checkmate. Clearly 1.Bb1 is a ridiculous move for White, but it is legal.
As for the endgame K + N + N versus K, computer analysis proves that it is impossible to invent a legal position with a forced checkmate in two moves. Checkmate in exactly one move can happen after the lone King makes a 'ridiculous move'. That is why the 50 Moves Rule must be invoked to force a draw.
This comment refers to forcing a draw in seven more moves ACCORDING TO THE FIDE LAWS OF CHESS. Consider another position: WHITE K(a1) and B(d3), BLACK K(a3) and N(d2), followed by the moves 1.Bb1 Nb3 checkmate. The endgame K + B against K + N may be a 'common sense draw', but it allows the possibility of checkmate for either side (after some truly bad play). Thus thus such a game will not have to end until the 50 Moves Rule has been invoked and before that happens either player could forfeit the game by exceeding the time limit.
According to the FIDE Laws of Chess, Article 9.6,
The game is drawn when a position is reached from which a checkmate cannot occur by any possible series of legal moves, even with the most unskilled play. This immediately ends the game, provided that the move producing this position was legal.(Emphasis added.)
I am rating(answering) the comment about diagram #3 on 2005-10-11 saying the King should take the Bishop, because 2 Knights & a King can not mate a King. That is not true, 2Knights & a King CAN mate a King.... White King is in 1A, one Black Knight is in 3A, the other Black Knight is in 2C, the Black King is in 3B. B.Knight in 2C has W.King in check. B.Knight in 3A covers 1B, B.King covers 2A & 2B...Mate.
I have a query that Is there any condition in chess where number of moves during mate process is reduced?
David, Since a King cannot move to an attacked cell, it could never attack an opponent King. But it can participate in the mate by restricting the movement of the opponent King.

Just a simple comment on the last endgame with the pawns: It is hardly a difficult endgame. A player of 1300 Elo would spot after 1 or 2 minutes that by playing the king to e7 and sacrificing the rook on the bishop, wins instantly. For anyone that is curious there is mate from the initial position in 17 moves (this is how easy it is).

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Indeed. Or move the Rook to f8, King to e7, and capture Rxf7. This obviously is a nonsense example.