A thick coat of mud can fix anything but this certainly doesn’t look professional.

Slow motion disaster. Pay them off and tell them they don't need to come back.

Some of it looks passable, but some of it is offset from the existing sheetrock enough to cause appearance problems when it is finished. In my experience, a bowed wall is usually the result of warped framing, and sheetrockers don't usually assume responsibility for fixing this. Receptacles that are too recessed can be brought out, but may need box extensions to meet code if they are too deep. Again, this is usually not the responsibility of the sheetrock guys; it's a problem with whoever mounted the boxes if they aren't set out properly from the face of the stud (typically 1/2" out...the thickness of the sheetrock).

His fastener schedule look about right (page 11). When you're tying new work into old, there are going to be some compromises. You may be surprised at how well the finished product turns out. He was hired to install drywall to the existing framing, not straighten said framing.

Walk it with the drywall contractor.

• Corners will have bull nose. They're fine.
• Bowed walls are typically due to framing that hasn't been straightened, or a plate, etc. Drywallers don't fix but ask if drywaller has suggestions. Your responsibility.
• Offset could be the beveled edge of drywall (for taping) or they installed 1/2" next to 5/8" - ask.
• Edges need more nailing