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.

Your paint problems could just be old or moisture issues.  

I’m no mold expert by any means and I always consult with someone on each project but it’s usually as simple as stopping the source of moisture and removing anything with the mold.

Just looks like a lot of moisture was on the walls. 

I'd say review this document put out by the US EPA and decide for yourself how much work you really want to do.A Brief Guide to Mold, Moisture, and Your HomeThis first document discusses how moisture happens and how it supports the growth of mold.Mold Remediation in Schools and Commercial BuildingsThis second document is the "all encompassing guide" on how to manage and remediate mold from all types of buildings (residential too).

Moisture - Did you know, on average it rains 28 out of 31 days in July every year in Bham??