T.S.
How old is the daycare provider's child? My son was bitten once or twice by oru providers daughter. It didn't bother me much, (I acutally thought good, if Vincent bites, at least he wasn't the first). Some kids go through a biting stage. My provider felt horrible about it and when it happened the second time, she said she was going to take the weekend to try to figure out waht's triggering it. In her daughter's case, she was at an age where children become highly agressive. I think it's between 25 and 27 months-but I don't remember for sure. And her older daughters were home for the summer and fighting a lot and her youngest was getting stressed by the fighting and that was attributing to it as well.
Since she looked into it and had a better understanding of what was happening, we haven't had any issues.
If it is concerning you, see if she can call her reviewer and see if they have any ideas of what could be triggering her daughter or see if she's willing to try to look into what's triggering the agressiveness in her daughter. If she's just over 2, it might just be the phase, but she should be able to work with her daughter and the biting.
As for the biting of himself. Try something like saying, "owie" why are you biting yourself. it's not nice to bite. Or if you see him biting himself, cover the area and say no, we don't bite, in a concerned voice. He may start understanding it's not good to do after a few times. If he continues, you could call the pediatricain for advice.