We are having our roof replaced due to a bad hail storm we had a few weeks ago. The roofer has the tar paper on the roof but then it started to rain yesterday. Today on Christmas Eve of all days our ceiling is wet and some drips from a door frame from where the roof is leaking. My Question is this, is it OK for it to rain on the tar paper and is the insulation and the ceiling damaged now that it got wet.

Tar paper wet is fine
Insul. Wet no good that area needs replaced.
Damaged wet ceiling section needs dried out or replaced. Either or the water will stain the ceiling and it will need painted.

Roofer should have put a tarp down. You have o make sure the roof is thouroghly dry.

Well hope this roofer was insured, most would have put something else up. If your ceiling is wet, most likely all of the insulation and even parts of the ceiling will all have to be replaced now.

The ceiling and wall bubbled out some but as it dries the bubbles seem to go away. The door to the closet still won't close however. The roofer is replacing the insulation. I'm just worried about mold or will it be OK because the winter aire is dry. Also will I have problems later on with humidity in the atic.

The "winter Air" is frozen not dry that way. I suggest to physically dry out all wet areas before any close up. The "ceiling bubbled out" means the water got underneath the latex paint depending how much bubble it is it may not stick long crap shoot there. Yes you can have problems of humidity in the attic ot needs dryer all of it to maintain its level of airing out its 'natural" moisture if it got too wet its like a roof over a pond and a mud hole and look how long with no sun a mud hole takes to dry. Best be safe . Now don't go up there and stick a 85,000 BTU heater in these and burn the house down. It needs to be wormed up slowly and evenly. This way you don't expand the drywall ceiling and warp the rafters. Slow and even. The door swells because the bottoms are always forgotten when its painted, Some water penetrated the latex but the bottom is the big player and top if that was forgotten.
Good Luck!