Dab a bit of primer on the screw heads.

The pearlite idea mixed in ceiling white paint might work.

The popcorn in ceilings is actually drywall mud in many cases. The mixyure is sprayed on with a special sprayer. You might be able to use a heavy spackle and dab each spot with a sponge or towel.

A couple of years ago we had to fix our popcorn and ceiling and what really worked well was to get some spray on glue, styrofoam (from a packaged whatever) and white spraypaint. So first we sanded the area smooth, completely covered the stain with primer and paint, next with a rasp, shredded the styrofoam until same size "bumps" are in ceiling. When paint/primer was dry and stain completely hidden sprayed on spray adhesive, with a small of amount of shredded styrofoam blew it at the area until it matched ceiling, when glue was dry, we spray painted the styrofoam with white (careful, too much spraypaint or too heavyhanded will dissolve the styrofoam). when dry, you can then paint with ceiling paint to match the rest (in case it doesn't). I know it sounds like a lot but it is really simple. We tried a couple of the popcorn in the can solutions but it didn't achieve a nice look in the end or a look we weren't happy with as we were putting the house on the market to sell. You can also practice on a small piece of board and hold up to the ceiling to compare.