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)?  

If a spot appears wet there is equipment called a moisture meter that reads how wet currently the area is.

I know flagstone has issues with moisture over time, hence it starting to slant or slope.

If you want carpet, go with a super cheap frieze and get a good quality pad with a moisture barrier (8lb pad).

I wanted to get the opinions of all the smart people on this forum on whether the rest of the stained drywall really ought to be removed (to prevent further problems, e.g. mold), or if it would suffice to just to let it sit for a little bit longer (i.e. to make sure any possible moisture is dried out)  before applying kilz and painting over it.

I don't have anything to offer with your question beyond what everyone else has said but I just want to let you know some general rules with foundations:1. crawlspace - cheapest to repair, good for plumbing because they can run underneath the house and easy to repair, bad for really cold days, pipes could freeze, some people complain about moisture in crawlspace and tile cracking but that's a long term issue and you may not have to deal with that and if you do, just lay LVP2. slab - second cheapest to repair generally, worst for plumbing because to fix, you have to often remove flooring and drill into the concrete to fix leaks and I've had a house that I played whack a mole with an active leak3. basement - most expensive to repair, okay for plumbing, but your basement could leakIMO crawlspace is the gold standard for foundation for rental investments in older properties (older than 1950s).