Depends by which rules and standards you are going by. Some say no and if you take another piece to get out of check-mate then it was technically just check, other rules state that its check-mate if all other avenues of movement are blocked and the only way out of check-mate is to take the piece then yes it is possible.
The objective of chess is to checkmate the king, where the king is in check by a piece and it cannot block the check, move to another square, or capture the piece checking the king.
The goal in chess, or the object of the game, is to checkmate your opponent's king. A king is in checkmate when he is attacked and no matter what move he attempts to make he is still being attacked (or in check). There are three ways to get out of check: move the king to a safe square, capture the checking piece, or block with another piece. If a player is in check and cannot get out of check, he is in checkmate and has lost the game.
In chess, a checkmate move is a move that one makes that puts the opponent in a position where the king piece has nowhere to move.
You can't checkmate another king unless the king is the only piece left on the board.
A legal check mate in chess is anytime the king piece is in a position that cannot avoid capture by the opponent's pieces. A legal checkmate signifies the end of the chess game.
Checkmate is where your opponent can neither counter or evade capture - checkmate .
Checkmate comes from the Persian phrase "shah mat," which means "the king is dead."
The term checkmate is an alteration or Hobson-Jobson of the Persian phrase "Shāh Māt" which means, literally, "the King is ambushed" (or "helpless" or "defeated"). It does not literally mean "the King is dead", although that is a common misconception, as chess reached Europe via the Islamic world, and Arabic mātaمَاتَ means "died", "is dead".[1] Moghadam traced the etymology of the word mate. It comes from a Persian verb mandan, meaning "to remain", which is cognate with the Latin word manco. It means "remained" in the sense of "abandoned" and the formal translation is "surprised", in the military sense of "ambushed" (not in the sense of "astonished"). So the king is in mate when he is ambushed, at a loss, or abandoned to his fate (Davidson 1981:70-71). The term checkmate has come to mean in modern parlance an irrefutable and strategic victory. Source: http://en.wikipedia.org/wiki/Checkmate#Origin_of_the_word
Yes.
Yes, just put the king in a danger that he cannot move out of or get another piece to move in front of
You don't have to say either. No chess rule requires it, and it may be distracting to your opponent or those around you in a tournament. If you achieve checkmate, you should offer a handshake, or do whatever you normally do to conclude your games, but you do not have to say "checkmate."
將死 [ Jiàng sǐ ] Which is literally "general's death" because in Chinese chess, the general is the highest ranking and most important piece, therefore the equivalent to a king in Western chess.