Cactus Game Design Message Boards

if an opponent plays mayhem while rain becomes dust is active, will they have to discard the cards they draw?

depends who has RBD activated. if it's your RBD, then yes, he has no hand. 

Correct. If you have RBD activated and your opponent plays Mayhem, then they shuffle their hand, then discard the top six cards of their deck (except Lost Souls). So RBD is almost as good as Lampstand for stopping Mayhem usage.