These don't appear to be booklice (psocids), but it's hard to see them clearly given their size. (We realize it's hard to take clear photos of moving objects this small.) They resemble mites, though we can't tell which type. We recommend working with a pest control professional since unfortunately we do not currently have an entomologist on staff at HGIC to consult with regarding indoor pest infestations.

Miri

I’ve had issues with mold and Mildew. My ceiling is covered in moisture from condensation and several items have mold on them including the chair they’re on? Could the be mold mites? 

Mites or even springtails (though they don't look quite long-bodied enough to be springtails) are possible, but we don't have enough information about specific mite types and identification characteristics to determine which they might be. Mold and mildew can definitely be a food source for these types of arthropods, however, so remediation of that issue (in addition to its direct health impacts posing a risk) is of course of paramount importance. If there is no moisture leak, such as from a roof leak or pipe leak, then perhaps use of a household dehumidifier (or several, depending on the space) will reduce any condensation so the environment is less conducive to mold growth and insect/mite populations. If the suspected mites are bothering the cat, involve a vet for treatment, especially since they might be able to ID samples under a microscope.

Miri