What they describe is common and happens all the time. But the most likely culprit is a loose spade terminal or high amp draw on the compressor. I have found that the Chinese capacitors do fail more often than others so if you want to change it you can but it isn't really necessary.

No harm in replacing the cap. I presume they're not expensive, and it could have been damaged by the heat.

As for your surge arrestor, it's entirely possible there was a surge (although loose connections will indeed create heat) - unless the surge is massive, your suppressor will absorb the surge and continue to function. They are a consumable, however, and eventually a large surge will destroy it or, over time it will fail after repeated surges (many of which you'll never notice.)

Most suppressors are designed more to save you, than equipment per se (although it certainly helps, equipment longevity-wise.) Power filtering/surge suppressing devices that are aimed at saving equipment are very bulky and expensive.

It doesn't seem likely that a voltage surge which would melt wires would damage only one applicance in the house. My thinking is the capacitor broke down and in the process pulled a lot of current before it blew up. This could be caused by installing either the wrong size capacitor or one that had a lower voltage rating then required by the manufacturer's specification. A bad connection to the capacitor is also a possibility since it causes a lot of heat in a small area.

Did you see the old capacitor and did it look normal?

I did not see the old cap. Today I took the panel off and the new cap was not in the holder, it was just left sitting on the shelf.

"it was just left sitting on the shelf."

It might not fit.

One of the things about higher reliability capacitors is that they are larger.

The wires should be stiff enough to prevent much real movement.