Won’t the buyer pay for an inspection after making an offer?
Your real estate agent should be able to point out cosmetic issues and I bet even if you have an inspection the buyer will get their own done anyway and odds are he will find something the first one missed.
I hate doing that in an empty house much less an occupied space. You can use hot mud and do it all in one day but I don’t think it’s as easily sanded as the standard joint compound
Crown moulding eliminates the need to finish the corners where the ceiling meets the wall, and I started drywalling over it after a few messes removing it, the finished product is better in my opinion
Pull back the tile till you find solid subfloor and remove the first couple deck planks to gain access to the sheathing for replacement. Cut out the damage and replace then install door.