Test for continuity, voltage, current and resistance. Both analog and digital meters are available. A digital meter is simple to use, easy to read and inexpensive. Analog meters are not as easy use or read and are becoming obsolete.
An easier alternative to repairing the damage is to use one coat of mud and then cover the rough repair with a preformed medallion. A plastic medallion can be installed using caulk to stick it to the surface or using the fixture cover plate to hold it in place. You can also get a plaster medallion, these should be installed using setting joint compound or plaster of Paris to attach it to the ceiling. Keep pressure on the medallion to hold it in place until the mud has set.
Pry the molding off the wall working at each stud. Drive a broad chisel-type joint knife between the baseboard and wall. Pull out on the handle several times to loosen the molding enough to wedge a crowbar behind it.
The best way to remove the insulation without nicking the copper is to use a wire stripper. Most strippers have a set of cutters for the most common gauges. Gently twist the strippers back and forth once or twice, and pull the insulation straight off the end.