Walls and Ceilings - great room drywall repairs

Our house is built over a basement. The great room with its high walls has settled considerably.
On one wall there is a hairline crack completely around a whole sheet of drywall.
On the opposite wall there is an area between the breakfast bar and closet that the drywall has compressed and buckled ( about 1/2 inch wide, 30 inches long) due to settling. Inaddition the corner beading above the bar is heavily cracked on both sides. the one side is the textured soffet (part of the mud has separated from the beading)

what is the best way to repair the hairline cracks?

what is the best way to remove and repair the buckled area?

what is the best way to fix the crack down the length of the corner beading (this side is painted)?

what is the best way to fix the soffet side (this area is not painted, just some kind of very white mud)?

If the sheetrock has compressed and buckled, then I would recommend that you have an engineer look at your house to see if there is more of a problem than sheetock. It takes substantial force to compress sheetrock to the point that it buckles.

The damage along the beading will need to be removed and redone.

The hairline crack can be taped and mudded over.

The buckled part I would cut along the line of the buckling and remove a slice or so until what remains is flat and set a patch in place, tape and mud.

the buckling was not as bad until I finished the basement and drove a wall right under the main floor wall. So I really got compression from the original settling and then more from forcing the floor back to level.

is the material used to stomp the ceiling different from regular joint compound, it seems whiter?

Sometimes it seems whiter because some mix paint with it to avoid a separate finishing step.

Chris has given you some sound advice. Let us know how the project turns out.

Thanks very much for picking up my slack Chris, been a very busy couple of wks. Much obliged, you sure you weren't a drywaller in a former life? ;)