they will replace the door and for the paint, yes they have to do the complete side. Remaining panels would be sand buffed and then only a light clear coat will be sprayed on the un damaged panels, just to match the color shade and gloss. if someone will only paint the door and bottom lining, it will look different from other panels.
And yes the bottom lining can be repaired. When i purchased my civic 06, it had side skirts installed, later on after 3 years, right side accidentally hit on a main hole and the skirt was down. then i saw a dent on that panel which was hidden by using side skirt. So I got it repaired from HONDA. My advise is to get it repaired rather then using a side skirt to hide it. in case you plan to sale and then my scenario happened with you, you ll be remembered by bad names lol.
Regarding the rust issue, if the job is done properly and the Filler, Primer and Color are sprayed in a proper way, then you do not need to worry about anti rust coating. as four layers of filler, primer, color and clear coat are more then enough to prevent it from rusting.