The latter required a skim coat to cover up which the security deposit did not even cover.

YOU most almost always will need to refinish the drywall by skim coating.

I was quickly skimmed this in about 30 seconds and it looks very comprehensive for a checklist.

I have read painters say the best way to “remove” wallpaper is to skim coat with drywall compound.

You can't change someone's mindset, only they can.If it were me, I would only buy bread, milk, peanut butter, and jelly. 

Old plaster jobs often did not have a finish plaster coat if you were wallpapering so you will have to do a skim coat.

Secure the old wallpaper and have a drywaller skim coat over it.

When we moved up we moved into an ex barn that had been used to house milk cows but had been converted to have a kitchen area and a toilet.

Your best best for both time and money would be to primer the walls....I would recommend you clean the walls with a bleach mixture (simple wipe down prep)....then skim coat the walls in areas where it is uneven.

If that doesn't fly you could always suggest to the owners that they milk the place rental wise and when they die let it go to a tax sale.