I was testing smoke detectors (hard wired into the house, says photoelectric on the back), and I sprayed insect spray to test them. I didn't realise then that you weren't supposed to use anything other than special test sprays. What now?
The paint is probably feeding the mildew, some paint compounds are like food to mold and mildew. You can paint over these surfaces with a product like Kilz. These links will help you out on framing and drywalling your basement.