There seems to be a problem with my game Game 9225411, as my opponent is shown to have moved on the picture of the board, but 'My Games' still claims that it is my opponent's move.

On my screen that game shows an error message "this game has an incomplete history and may not be recorded correctly". Something appears to have gone wrong with your opponent's promotion-to-queen move, which is recorded in the move list but not on the board. You could try sending feedback, perhaps it can be fixed. Otherwise, you could arrange with your opponent to play out the game as a "set piece" game starting from the correct current position.

same thing with my game 9346816. something about promoting a pawn i suspect. he moved, tried to promote a pawn...the board shows his move, put his comment under my name, and still says it's his move!

Suggest the two of you send feedback, sounds like something needs fixing in the promotion process.