Electrical – Is the insulation on this cable burned

You may be able to find a UF cable that has a rodent repellent in it, but it's certainly not standard. I have never seen it advertised on UF product packaging. I have heard that some datacom / telecom cables that claim to have a rodent repellent jacket, and I have seen those same cables chewed to bits by some varmint that didn't mind the flavor.

If you are going to run power in conduit for rodent protection, you don't want to run UF, run single conductor wires rated for wet locations, such as THWN. The only thing I can think of more troublesome than running NM in conduit would be UF. Seal the conduit well at the ends to deter the little buggers from creeping down the pipe, they can infiltrate smaller conduit than you'd think.

I'd usually rather run conduit anyway with a buried cable. If a rodent does eat your wire and it's in conduit, it's not too bad to pull a new wire. If it eats direct buried UF, get your shovel.

Loose connections can produce heat and cause this problem. The fix is to disconnect and reconnect properly. Spring-loaded "stab connections" are particularly likely to suffer this problem; screw terminals (or shove-in terminals that are clamped by tightening a screw) are more reliable. If in doubt, outlets are cheap and you might want to simply replace this one.