First you need to cover the 2 hole. You need to attach the replacement piece of drywall on the big hole to something solid before mudding and taping it. 2 choices are to open up the hole larger until you have some wood to attach it to or improvise! My favorite way to improvise is to cut 1 or two thin boards about 2-3 inches wider than the narrow width of the hole. Stick it up the hole the long way and rotate it so it is resting on top of the hole with about an inch on either side. Hang on to the board in the middle through the hole and put two screws up through the ceiling on either side of the hole to hold the little board in place. Screw your new piece dry wall into the little board(s) you put up there. Tape and mud. Can't tell how big the little hole I but I would probably jut dry to put a piece of mesh tape over it and mud. If it sags you might need to put something up there to back up that patch too or purchase a firmer patch to go over it. No need to prime anything until you get all your mudding and sanding done. Use a putty knife and scrape as much loose paint away as possible. I would do little to no sanding of the paint edges as you are sanding paint with lead. Just skim coat everything with mud. Patch, tape your corners, mud everything (couple thin coats) and sand. Then prime and paint. Your joint compound will be perfect for all. Wear a dust mask when you sand.

If the sheetrock meets the ceiling, you can caulk that joint with firestop caulking to achieve the results that mac mentions. It's easier and not messy. Michael

Ok, got it. I still think there's some moisture in that joint and the topping is making a barrier so the moisture can't get out. I read that it's vinyl-based so that would make sense. Anyway, you can try to knock off the bubbles (or cut them open with a utility knife) and touch it up with easysand. If the fiberglass tape is also proud of the wall, you might have to pull off that portion and redo it. During your sanding, it's helpful to hold a light on the side to reveal the defects, etc.

I have a drywalled porch ceiling. 1968 house. Something happened to cause the fasteners to fail; a roof leak or termite damage are the first things that come to mind, speaking from experience. Have you tried screwing a new drywall screw along the joist? If the joists are badly damaged, it won't hold. Again, speaking from experience with hidden termite damage. I'm not saying your house has termite damage, tho. ETA: I look at your pictures and it looks like a moisture issue as GN Builders said. Try screwing a new drywall screw near one of the nails to see if it will hold.