OTB Chess Rules Questions?

I have not played in many OTB tournaments, but I have not heard of such rules. For (a) if the opponent of the person who made the illegal move notices that it is illegal, that opponent should reverse the clock immediately and inform the illegal mover that his clock will continue to run until he makes a legal move (preferably with the touched piece). For (b) that's not as much a chess rule but a venue practice, and would vary from one venue to another.