If it's mold, it's it just that spot or can you find the cause of the moisture feeding the mold? 

We communicated every detail continuously, and even bought a dehumidifier to take care of moisture in the basement.  

They are quicker and moisture is not getting through an overlapped seam..not a chance.  

Is there a water/moisture problem etc.... or do they just want cosmetic work done? 

In real cold climates it may be more involved due to moisture concerns.  

I bought her a damprid to get rid of excess moisture and told her she should have opened her windows to ventilate and that she should have told me right when she noticed, but she waited several days until she finally paid her rent, after it was past due.

They just replaced it too, but didn't put the right kind of moisture barrier underneath for Utah.

You shouldnt have a big problem getting rid of the skunk smell especially if your remodeling and replacing carpets etc and painting but I would use a Kilz or my favorite is Bullseye 1-2-3 (has a stain, mold, moisture, and odor blocker). 

Likely cause is a broken seal which could have been sealed to stop moisture intrusion to this extent and avoided window replacement.

I don't see major issues during a quick walk through but wanted to get your opinion as it seems there are a few cracks on both sides of the house denoting signs of settling/moisture/etc. and some crumbling (pictures below)?