Well that kink or flat spot could be hammered out under tension. Hook the one end on a tree or post or something heavy. Strech out the cable under tension, then with a 4x4 or bigger post that you can put under the cable so it supports it. Then hammer(not a sledge hammer) the cable until it rounds out again. I have done this a couple of time to the TT trucks winches. As for How much it can be damaged. If I remember right, if 20%(or more) of the cable is damaged then it is time to retire the rope. So if the cable is a 7 strand one, that would mean 1.4 big strands have to be busted to meet this requirement. If it is a 13 strand one(smaller strands), then 2.6 strands would need to be busted to meet this requirement. So I think if one full strand was busted on a 7 strand one I would retire it. What I saw in the picture is a single strand of one full strand(ok in my book).
As for the popping and such, this is the cable stretching or elongating or those areas where you have kinks working it self back in shape. I would not think it is stuff breaking unless it is real old cable. Which brings up a whole different subject. If I bought a used winch and did not know the history, I would trash the cable and just put a new one on for my own protection(maintaince).
As for a shorter rope on the drum, I would agree with this. It makes sense in most of the times I have used a winch a shorter rope would have been a better choice. With a syn winch ext to have to have more options when needed.