There's "setting" compound, and "drying" compound, with variants.
Former is dry- you mix w/water, and it reacts with water and hardens.
Latter dries (& shrinks some) and hardens in the process, IF conditions
are suitable for drying (temp, RH.)
IME, either will stick to pretty much anything, especially exposed
sheetrock gypsum layer.
Second, the paper on sheetrock provides some/most of its physical
strength. And ... even if the paper is left in place, sanding it makes
for fuzzy final product. DAMHIKT. Paint will seal the gypsum layer,
but will take a few coats
Sure sounds like some wall sections should be stripped and redone
properly. They could write off the earlier sessions as OJT. Can you
find someone local who can inspect and advise?