Is it necessary for the surgeon to shave the existing hair on the part of the head where the transplanted hair will go?

No, but it makes it easier for them to see what they're doing. Might not make a difference at all in the end but if you going to do the surgury you might as well do everything you can to help. Unless the tranplanted hair is being put in an area that has no hair. Shaving is used in spots when hair is thinning.