Weird game result claims

In general, weird game result claims are covered by Article 5: The completion of the game.

Questions

Q: The arbiter is called to the board. The players ask the arbiter "is this checkmate?". You look at the position and the game is indeed checkmate. What do you do?

A: You DO NOT declare the game as checkmate, because this counts as giving advice. You ask the players to come to an agreement on the result, because players have to come to an agreement on the result which is then passed to the arbiter.

Q: Two players play a game and reach a stalemate. None of them notice and continue to play on until they reach a checkmate. Eventually, they realize that the game was a stalemate earlier on. They explain this to the arbiter. What do you do?

A: The stalemate stands, because everything else is irrelevant. This is covered by Article 5.2.1: The game is drawn when the player to move has no legal move and his king is not in check. The game is said to end in 'stalemate'. This immediately ends the game, (provided the stalemate move was legal)