First, the easy question. If the roof's sheathing is extremely wet, it would be good to have the roof dry out. This may, or may not, involve removing some paper. Depending on how wet the roof is, the paper may not need to be removed. It's a tough call w/o knowing or seeing more.
As far are replacing, or simply repairing, the paper that's already in place, you need to understand its use. It's meant to keep the roof dry in the event any shingle were to get blown off. Also, it's meant to keep the roof dry until the shingles, themselves, get installed (which is your situation.) If the paper is a bit wharped, I wouldn't worry too much because after time, it should lay flat when the sun heats it AND the shingles are installed. HOWEVER, in areas where the paper is badly torn (or missing), it should be over-layed (or replaced.) Again, the paper is there for a reason. Use your gut feeling and INSIST the paper be over-layed / replaced where there's 'heavy damage'. Just remind the builder that you're worried, and are aware, that shingles DO get blown off and, if that happens, the roof will leak! (Tell him you don't care if insurance will pay for it; you simply don't want your roof to leak.
If he insists on NOT doing it, take pictures of the roof's damage being shingled as the installer puts on the shingles. If you can, get up there with the camera and take CLOSE-UPS. If he asks what you're doing, telling him you're covering your Butt in case the roof leaks. ANd that if there is a leak, you'll need to prove negligence. Or, just tell him you want the 'job' to have a video record.
I'll see if I can get some legal advice for you. For now, my best to ya and hope this helps.