You have put a lot of work into this and it is shaping up nicely, and I for one can truly appreciate the level of work and pride you have put into this project. From the pictures it appears that air will be able to pass back and forth over the new wall into the cavity behind via the joist cavities. This air movement will still take place to some smaller degree when a ceiling is installed. It is unclear at this point whether that cavity will become a moisture issue, this will be dependant of the humidity level of the basement and how damp the exterior basement wall and floor gets from foundation leakage. Although it is to late now I may have been very tempted to have the existing foundation wall sprayed with 2 Ib. foam insulation including the header cavities, to the floor before the dry was applied. Once the foam is applied to at least a 3" thickness it not only insulates and air seals it also becomes a vapour barrier. So the foam application would have solved many issues with one shot also including inhibiting mouse movement. Header cavities are notorious air leakage and heat loss areas, and a great area for mice infiltration. The fact that you appear to have laminate flooring and it does not appear in the pictures to be moisture damaged is a very positive point as laminate flooring has zero moisture tolerance.
Anyways at this point all one can do is press on and see what develops or more importantly what does not develop. From the looks of your workmanship thus far I am sure it will great man cave reloading room when completed.