Listen to their problems and find a solution.A side note: have thick skin, people will not be looking forward to your call.

Most of it is simple, but my biggest concern is the walls on half the walls have this thick, chunky texture.

But if you don't want carpet then a good quality, thick (expensive) underlayment would be your best bet.

The biggest issue I've found when using deal machine is that since it's a available to everyone, once you reach an owner they are fed up by all the marketing they have received and are ready to lay it on thick on all future callers.Anyone can drive by a neighborhood and think they spot a "diamond in the rough" when they see overgrown weeds, an abandoned vehicle, or other deteriorating conditions. 

It also tells me when there is thick black smoke, there is usually a fire :)

Depending on the thickness of the plaster, you may need to use 1/4" or 3/8" drywall in your patch.In the picture it looks like there has been water damage in that location at one point in time.  

How many SF of sheetrock need to be replaced (thickness, type, and cement board). 

I'm hoping that the egg crate, with a thick mattress cover or even a comforter underneath a mattress cover will do the trick.

I am looking at a ≥1000sf, 2ft thick walled and gated tiny property in the Peloponnese, Very private, great price, but it has some issues - are any of these a deal breaker - 1000ft stone paved foot path from parking (with wow views), low ceilings in (lower) bedroom and bathroom area, l.rm is beautiful with tall ones, has a lovely terrace and lovely sea views.

The reason:- It is low odor so easy to work with- Very thick so coverage is great plus no drips so you can paint faster- You can keep paint color on file linked to the address.