The insulation gas will all be gone, but if done and sealed well you won't get any moisture inside that fogs up the glass.

Mold comes from moisture.

We've brought in two dehumidifiers which are helping, but I'm not sure what the root problem is or even who to ask for help.One contractor said moisture is coming through a hole in the exterior stucco, but another said no way because the vapor barrier would block it. 1st one recommended installing insulation, but I've also read this can increase condensation problems.

There's moisture getting in somewhere -- that's what's warping the floors. 

With the sun beating down on roofs year round, or leaves falling and sitting there causing moisture to go under the roof and rot wood, the usefulness of shingle roofs is not a lot over 10 years.  

The meter will detect the presence of moisture.

I don't know if all the moisture in this photo was because the floor is soaked or if this is because they sprayed it with something.This is quite an aggressive home renovation they have done without even consulting me. 

Laminate still has wood dust in it that can warp when exposed to moisture.

I imagine the allure type flooring would hold up even better to moisture but it's also about 1.49/sqft whereas laminate can be had for 0.29/sqft for something that might last 5 years and under 1/sqft for stuff that should last longer than that.  

Tenant agrees to allow Landlord timely access to premises to do maintenance and repair.Tenant will notify Landlord in a timely manner of any damages or problems as they arise, including damages caused by Tenant, malfunction of appliances or fixtures, and water/moisture leaks and spots.Tenant will take care of the premises, keeping them clean and clear of debris.