To fix problem #1 - nails backing out of the ceiling - pound the nail back in and then drive a drywall screw in right next to the nail (so the heads overlap) that will hold the nail in place and hold the ceiling up better. (or you can pull the nail, but it may bring some plaster with it.) Of course, you'll have to plaster over the screw/nail.
Getting rid of stucco? WHY? it's lovely! - Sorry, I don't know of a way to do that that isn't messy. I've got contoured ceilings in my house - can't stand them but not worth the effort to change them.