But if green played two games in a row where blue makes the same blunder(c8 or d8) then he will be play-banned for 2 minutes just for playing the best move to resign and abort the game
Share your quickest checkmate. or your favourite one.

и играл он довольно глупо
This is no checkmate.
Qeg7# checkmate

You didn't checkmate them: Green obviously abandoned the game, you as Red went for the 20 points (that wasn't going to be granted) and Yellow being a novice moves their Bishop to threaten your Queen as they forget on the next cycle Red moves (and would probably capture the Bishop) first than them.
I know I'm relatively new and inexperienced, especially in 4pc, but I don't think you're correct. Red moves up with their king's pawn, blue moves, and yellow moves. Green pretty much blunders, which lets red capture their queen. However, they can't recapture it before yellow protects the queen from danger with their bishop, making the king unable to move. The queen is checking the king, and nothing is able to capture it.
So the best move for green is to abort the game