But if you are storing items that may carry some moisture, cedar alone won't meet your need.

Regular framing and building wood is kiln dried down to a low level of moisture, regular paint is designed for this.  

It looks like a moisture issue.   

Some people love that heat because it keeps the moisture in the air.

I'm working on a rehab for rental and pulled up the flooring (vinyl floor and carpet) and noted there was a ton of moisture (wet) in the existing wood floor.

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.