I still remember how it stank (no respirators with organic vapor cartridges to be had).

If you can follow the pipe into the basement or similar, you can verify if it's connected to a gas line.One thing to watch out for on "ventless" gas anything: if you use it a lot, you'll put a lot of water vapor / humidity into the house.  

The house has work needs to be done with support beams (rotted) and a lot of rotted siding spots where new wood, insulation and vapor seal need to go up. 

Different contractors I work with have grumbled about internet plans and how they dont have room for insulation  or the vapor barrier details are all wrong for the climate zone we live in.    

On the slab cut for new plumbing drain lines, which was maybe only 5 square feet of slab cut away, nowhere near the footers, exterior walls, or any structural elements, they not only had to inspect the new drain pipes in the ground as expected but then also to inspect for termite treatment (totally ridiculous), rebar  (in a slab with no existing rebar), vapor barrier, and then the final pour.

Sounds to me like the insulation was installed incorrectly, and the pipes are outside the insulation, or there is no vapor/air movement barrier. 

--Sometimes, humidity or dampness (water vapor) in the air can supply enough moisture for mold growth.

They are really good to insulate and create a vapor barrier in hard to insulate spaces.

You may also want to incorporate a vapor barrier between the brick and rigid foam. 

In addition, the ground is exposed with no vapor barriers over the dirt.