Do you have an idea of the R-value of the insulation you put in? I'm wondering what this will take to heat and cool during the peaks of summer and winter.
Those are 2x4 studs, so R13, shoving thicker insulation in doesn't change much.
True. Depending on how heavily they compressed it to fit between those studs it will likely be less than R13. No matter whether you use fiberglass or rockwool, you should make sure you buy insulation sized to the depth of the cavity it will insulate. Then use an insulation knife to cut in for obstacles within the cavities.