Is there a question pool for all of the games?

No, there is not a question pool for all of the games as the game mechanics are different for each game. You can copy questions from the same type of game to another by copying a game. When you are in the Game Info tab, towards the top right hand side, click on Copy Game, and then name it with a different name. You can edit the copied game just like you would any other game. And then be sure to Save periodically.