sorry I didn't answer all your questions in first reply

Do higher ranking chimps take the "best" and leave less desirable parts for lower ranking members of the hunt?

It's unclear. A good amount of data says whoever begs the most (i.e. harasses the holder) gets the most meat. Other data suggests that maybe chimpanzees may share reciprocally, a chimp will give more meat to their buddy and in turn may get meat from them later. This form of reciprocal altruism is extremely rare in nature and needs to be tested further.

Or can researchers collect what remains to perhaps learn how they hunt and consume?

Yes, but this is tough! I can't think of a systematic study on this, probably because we can't recover carcasses since they love them so much. Ethically, tricky to obtain and test wild meat nutritional content.