Pull down the drywall until you get to drywall with zero moisture damage.

or breathability and recurring moisture too ?

If there is damage (extensive moisture, cracks, holes, etc) is may not be a bad idea to replace. 

This will ensure that errant mold spores do not migrate from the containment area into surrounding areas.)Will you repair the source of the moisture or do I need to call another contractor?

., painting over brick is not really maintenance friendly, as moisture (winter) will tend to push the paint away from the brick, even with a good paint, not to mention if your painter only knows how to spread it and doesn't know which primer to choose. 

That definitely eliminates the possibility of wood rotting etc due to moisture in the future...  

All that hot air and moisture running through the pipe for years is bound to do some damage.

That does look like it could be the sheet of underlayment that is high and the door has scraped away at it - check the bottom of the door - it will have matching wear marks.If that's not it, then perhaps it was a chemical conflict... certain vinyl and rubber can often be incompatible when moisture is introduced.  

Is there a lot of moisture on the windows?

We removed a large tree that towered over the roof causing a mess with falling debris on the roof and blocked all sun which left too much moisture.