Which comes first painting walls or stippling the ceiling

Short answer flat.

The unfortunate thing is flat tend to require more touch up as you can't wipe things off like you can with paints that have a sheen.

3 years I would just repaint the walls but if you are really against it here's what I would do. Use flat paint or an eggshell at the most and re-roll the walls with a thin quick coat. You can get away without cutting in the outlets, baseboards and ceiling. If you use flat you can probably touch it up with a small nap roller pretty good just feather it out really well.

The damaged area could have been the place the shower head pipe may have originally projected out of the wall. When the rain type show head was installed it may have been moved to a lower level.

If this is the case then the damage that you see is just a shoddy hole repair. Fixing it up so that it looks decent will involve scraping, sanding and repainting the area as a minimum. Worst case it may mean removing the old patch and filling in with a replacement patch that was done correctly. Patch technique will depend somewhat on the type of wall it is. You mentioned plaster - is it on lathe or plaster backer board of some type?