Toy snatching and naptime crying out

I have a new two year old in my care (just over 2 weeks now) who is a toy snatcher...every time he sees another child with a toy, he suddenly wants it very badly and runs over and grabs it...of course causing tears and frustration from the other child usually. Every time I tell him we don't take toys from our friends and that we must wait out turn and I make him give it back...but so far no change (he came from another daycare where his mom said he recieved no discipline). Do you ladies think it is just a matter of repetition or is there some other way of dealing with this?
Also, the same child, while he naps well, cries out loudly 2-3 times each naptime...soemtimes he goes back to sleep and other times I have to go and lie him back down because he is sitting up and crying at thetop of his lungs and I am worried it will wake the others up. His mom said he does that every couple of hours all night long too and she just ignores it. I would love to ignore it, but I don't want everyone waking up! Anyone ever had a naptime crier like this?

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!

I can add that for the nap, I would ignore it too. All my kids sleeps in the same room and I have one that would 'cry' out and fall back to sleep or simply continue to babble and chat in his playpen once in a while. The others get use to it and sleep through it.