Peeling and cracked paint

Personally I would scrape off all loose paint and then pva and fill with decorators skim and repaint

Yes, sounds like an ideal candidate for lining. Whether the substrate is lime or multi finish it shouldn’t require sealing. When you have scraped all of the blown paint off, buy a cheap moisture meter and ensure the ceiling does not have a reading of over 20%. If it is over this is more than likely the cause of the paint failure although this is rare. If the existing paint partially remains then you will have to feather the edges with a plaster based filler such as toupret interior filler, available from toolstation or dulux. You may need to carry out a second fill after rubbing down. Once the ceiling is prepared get a medium pile roller and size/ roll the ceiling with all purpose paste. This will ensure no blown seams. Finally use 1400 grade lining paper, well pasted and apply with the seams facing the primary light source. 24 hours later, roll the paint against the seam line in order to flood any gaps in the seams to make them as invisible as possible.

For the ceiling scrape off as much as possible it sounds like you have white wash then give it a sealer fill what needs filling sand it down then seal it with paste then you can apply lining paper Your walls just need filling and repainting

If the plaster is chalky it could be a sign of salt coming to the surface which in time would eat into the emulsion paint and cause blistering and cracking and eventual peeling . I'd personally scrape of the loose paint to a solid edge then use an oil based alkali primer , leave till next day then use fine powder filla to skim out the edges then lightly sand as not to pierce the primer then re paint .for a better finish use 1200 grade lining paper .