Sharks have a unique, loose jaw suspension that allows them to raise their snout and loosen their jaw from the braincase, thrusting it forward so that, in effect, the shark has a terminal mouth right out there at the end. But in reality, sharks rarely bite pieces out of a prey. Usually, they engulf them with their amazing buccal or mouth pump, which acts like a slurp gun. Cocos whitetip and lobster. Hard to say, because we don't know what pain means to an animal and can hardly describe it ourselves.
Some people are almost insensitive to pain, others are highly sensitive.
I have done minor surgery on sharks, and they seem not to feel it. So yes, sharks feel something we would call pain.