personally I think the use of rawl plugs for rads is a heath Robinson job at best and just done by builders to cut corners. You can pull a rad affixed with just rawl plugs off the wall very easily.
Either you’re using crap plugs or the wrong plugs.
The old rawlplug holes will probably still be visible as the plaster dries (it will dry faster / slower over the plugs). You can drill through the new plaster to the old plug at that stage before painting.
Depends on if your plaster is completely blown. My last “skim” was half an inch thick in places because the original plaster was just falling off the wall. Good luck finding your screw hole under that.
Time making good round some screws Vs rollering a flat wall.
Why would you need to make good the few mm around a screw where a bracket is obviously going?