How can I remove or cover a screw stuck in my drywall?
Turn the adjusting knob on the locking pliers so that it takes both hands to clamp them shut on the screw head and squashes some small flats into the screw head when shut.
Hold your locking pliers flat against the wall
Clamp them shut
Unscrew

You want the pliers so tight that you can barely get them clamped. That will get you the maximum grip on the screw so you can get it backed out.
You want the pliers flat against the wall (not sticking straight out from the wall) because it gives you maximum leverage to get the screw turned.
Once the screw is out, a little spackle will fix up the hole with no problem.
If the screw head snaps off, run a flat edge across the surface of the drywall to see if the screw is below the surface. If so, pretend it's not there and spackle right over it. If the screw is still sticking out from the surface, a small grinding wheel on a hand-held rotary tool (like a Dremel tool) will quickly grind it down to below the surface after which proceed like it's not there.