Braided fishing line as cord

Will that cut into tree limbs?

It would depend on the amount of weight your hanging i have hung up to 20lbs with no problem

Any problems with stretching?

Yeah, bear line is a problem in the ADK's. Mostly, the higher elevations, hills, are pine covered and pines make terrible bear hanging trees. The bark is often scaley and can catch lines easily if any pressure is applied. Hardwoods, are much better. But, the fine line can also cut into the bark leaving a scar, and catching the line. Generally, I use a larger line for bear lines, often removing the core and leaving only the sheith. Not so much for strength, but for the diameter of the line. there is a lot less damage to the tree and it is a lot easier to pull up. More complicated methodes can also be used. But again, in the ADK's, even with all the bears around, a good hang is all that is realy needed. In 40 years of camping I have never had a problem, anyway…maybe I am just lucky.

Nope it doesn't stretch and for pine I Carry a 4th piece of sheath from paracord that I run the line through so it doesn't snag or cut into the bark

I definitely wouldn't use superline for a bear cord for the tree damage thing (and because it's a pain to handle and tangles easily) but I do use it very regularly for the drawcord in my tiny stuff sacks (cuben stake bags, ditty bags, etc). Too small for a cord lock, so I just use a short length of cord in a tight knot around both ends of drawcord as a slider, it works very well and weighs literally nothing. I have a few small cuben stuffs like this that will only 50% of the time register on my .1 gram scale.