Drywall screw marks

if the screws weren't galvanised they rust and you need to seal the head of the screws with an oil base paint ie, undercoat or eggshell.

Rust from bud screw

Touch up the marks with an oil based paint (primer) then finish walls with emulsion

The heads of the screws need to be treated. Painting them they will just bread back through. An oil based product (topcoat or undercoat will block this first) leave to dry then touch in these bits a couple of times. I would then re coat the whole wall with another coat otherwise these patches may show up as touch ups. Re coating the whole wall will leave you a much better finish!

There's a lubricant on the drywall screws that can sometimes show a round mark where each one is , so it's an oil stain , you can get a zinsser primer in an aerosol can , I'm sure it would the bin primer ( check that where you purchase ) that would be the one to use , may have to spray over them twice though. You will need to touch up the primer maybe twice , I would recommend a 4" roller similar to the one you painted the walls with and recoat the walls again and you may need to do that twice as well.

Most possibly from the screws holding the boards on I would give it a light rub with sand paper then couple of coats of stain block then repaint