Re: ceiling - spray ceiling
You should also assume that there is asbestos, while many of us don't believe that this the harbinger of death that it's made out to be, it still warrants caution and safe handling practices. Having it tested is a personal call, homes build post 1978 are less likely to have asbestos products, but it is still possible.
The easiest way to remove it is to clear the room of furniture, tarp the floor with painters plastic that is taped at all seams and around the perimeter to the wall. Use a garden sprayer of water to dampen and soften the popcorn, then use a scra-per or drywall knife to remove it. When you're finished, simply roll the plastic up off the floor, put it into a garbage bag, and toss it. You should wear safety glasses and a good quality dust mask while doing this work.
Once the texture is down, you can repair the drywall, retexture to your liking, then prime and paint.
If all you want to do is repair the damaged areas, you can do this too, though the patches may stand out a bit when you're finished. Patching would be best left to professionals or experienced DIYr.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!