basement interior walls

[CATNHAT]

NEVER EVER EVER--put vapor barrier below grade. it traps water vapor and condenses creating the mold. in your case, it appears as though the window is leaking or at least condensating and the water is traveling down to the bottom plate. Rigid insulation is also a no-no as it does the same thing--traps the water vapor.

In addition, always use pressure treated lumber anytime wood is mechanically fastened to concrete--it appears as though the original builder used regular SPF--also a big time mistake. Any decent inspector will fail the SPF & vapor barrier combo.

50% humidity is to high as well. The acceptable relative humidity will fluctuate with exterior temps and 50% is too high during winter. Dehumidifier is imperative during summer months.

This Relative Humidity Temperature Is : Should Be Maintained
+40°F 45%
+30° 40%
+20° 35%
+10° 30%
0° 25%
-10° 20%
-20° 15%

Fix the leak, remove studs and plate installed on face--and replace with PT plate and SPF 2x4 on edge, R-13 batts, 1/2" rock.