Could you play a whitenoise machine during nap time so if he does wake up the sound would be muffled? That stinks he does it at home too...I would follow Mom's suit and just ignore it as well and pray the behaviour stops after he gets more used to the new environment.
As for the toy snatching, I would keep up what you're doing perhaps adding in a "stern voice/face" so that he gets the hint that it's unacceptable faster. It's a very normal behaviour for 2 yrs old and is just slower to learn for some than others. I have a toy snatcher as well, it gets frustrating!