Assuming you have clean holes with no damage to the drywall from over-tightening or pull on the fixtures, the half inch ones can just be filled with mud. I like the setting type for the first glob. For the one inch holes I like to cut a small scrap of 1/4" hardware cloth which I hold in place with a string attached to the center while I fill the hole with the setting type compound. For ceiling I just add some weight to the string until it dries.
Be sure to use enough force to force some mud through the wire cloth. This works much like the fingers on plaster and lath
The 20 minute, setting type, sandable compound is a good choice for the type of repair. The first fill should be mixed a little to the dry side, thereafter mix it to look and feel like regular all purpose compound.
Any holes over one inch should use a backer board and drywall scrap.
Get a box of spackle from the hardware store. Mix it up pretty stiff (pie dough). It is best to do it in a couple steps. Start filling the hole so it is about half the size, let the mud set up, sand flat and fill it flush. Sand that flat and you have a fix that won't crack.
In my experience, after removing the screw, the type of fastener that the OP is talking about leaves a threaded metal tab that is not flush with the wall. Any attempt to cover it up is doomed to leave a bump.
I've found three ways to fix that.
Method one: For modern sheet drywall, you can tap the fastener with a hammer until you create a shallow dent in the wall. Patch and sand the dent as normal.
Method two: Using a flat screwdriver or a sacrificial wood chisel, get the blade under the fastener, and tap with a hammer. The fastener will usually shear off flush. The remainder can easily be pushed into the wall cavity, although I would avoid doing so if it is above an electrical outlet or switch.
Method three: This method works very well with older style plaster walls. Take a pair of needle nose pliers. Leave the pliers closed. Insert the closed pliers into the hole (fastener). Wiggle the pliers up, down, back and forth. The fastener will break off flush with the wall.
First , do you plan on re-papering the room with new wallpaper ?? If not I would just hang something over the obviouse holes and forget about it..If you are gonna put new paper up , peel the loose paper around the hole and fill the holes with setting type compound...You can get a small box at Home Depot..Mix it in a coffee can or bucket a little on the thick side for the first coat..Mix just what you need as you can't save it as it will set in the bucket or can...Scrape it flush and fill again..Sand and repeat..Sand one final time and paper away...HTH...
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