Is there a muscle that wraps under the jaw/mandible?

Yes: it helps manipulate your jaw and helps you eat.

Yes there is: I believe that you are talking about the mylohyoid muscle when you refer to the muscle that wraps under the jaw/mandible. There are lots of muscles in that region but that one best fits your description of it's distribution in my mind.

Yes, a few: Yes, many muscles in the surrounding area. If you are having pain in the area, see an oral surgeon for expert advice.