Ditra matting
And bedroom looks like it has a door but no wall, primary bed misses the alcove where doors are, and all miss the doorways apart from bedroom that...
Firstly grind that lot all off, take a moisture ready see what RH it is , then go from there.
If you can't afford doing right then just leave it as anything you do with it will wasted time and money.
If the Magnasite was installed in the 50's > 70's then I would say anything under that is the same age. So I doubt you even have a sheet membrane...
Did you not have a look first, or was it just over the phone?
Problem you are going to have is once you start lifting around that area you'll be going all the way with it.
It looks like Gypsum so a cement based feather wouldn't be advisable.
longopac box 4 | Trade Discount Shop
Floorskills Green SET 5 Angle Templates | Trade Discount Shop
That machine you have in the picture is not heavy enough, also can't really see the 5 segments but they need to be split/crush type. A good vacuum...
Best option, leave your number with the clients for a later date. :D
I have this going cheap. Band new and works. Only thing is, the control button doesn't so it's on and off only. Green Laser | Trade Discount Shop