Re: Remove or just cover old drywall?
1 - Why does the drywall need to be replaced?
2 - Overlaying, while acceptable, is going to create clearance issues around windows and doors.
3 - Removal allows you to add insulation, check/add wiring and plumbing, etc. Starting from bare stud generally results in a better finish as well, since you are not going over the top of lumps and ripples that may be in the original drywall.
If it were me, I'd remove and replace, yes, this is messier and a bit more expensive IF you are not doing a portion of the work yourself, however, the finished product will be far better than an overlay.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!