If someone is jamming your power lines AND rf / wireless, you're under a full on assault. You're unlikely to defend against someone invested that much in breaching your home easily.
Although a Springfield Armory XD45 makes a wonderful backup :)
Or just cut the power to the home, arguably just as easy no? I think if your being targeted like that then you probably have bigger issues to deal with though...
No, because they send modulated signals over the copper power cables. Therefor, if they had their own backup power and were operating over the powerlines, they would work.
In most neighborhoods with above-ground power lines, it's incredibly easy to access the neutral wire.