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).

We have a problem with too much moisture in our home and the condensation build up in the winter is rotting the skylights wooden frame. 

I truly can only assume where the moisture is coming from.

We prefer forced air heat/cooling as the air movement provides even heat and helps prevent moisture problems.

There is a good moisture barrier underlayment and 2.)

I'm considering a possible humidity or moisture issue in the room because of my window A/C unit.