Just wondering if we  are allowed to have  two buttons that can change their actions. There will only ever be two buttons on the screen but they change what they do depending on the game-state.  An example: a button that +1 to total and a button that -1. If you pickup a powerup the first button now  divides the total by 2 instead of adding 1 but the total number of buttons never changes.

That's ok indeed.

Just imagine that the game has to be playable with a very simple controller which would offer only two physical buttons.

Wait, what about mouse movement to click on the two buttons. So the  buttons are physical objects on the screen (instead of key presses) and you move the mouse to click  on them. Is that allowed?  The mouse isn't used for anything else though.