You for sure don't want to prune them back hard......in fact, I'd recommend as little disruption to the climbers as possible. They should come away from their current support system relatively easily and I would just leave them in place in a mound while the fence is being rebuilt. Once the fence is back, re-hang the cimbers as best you can.......draping over the fence is a good way to encourage their reattachment. I'd suggest fishing line if you need something more secure.

The advantitious roots will appear from anywhere on the stem. Oddly, they seem to be most plentiful where the stems come into contact with something they can attach to - like the fence :-) You shouldn't have any worries.

You can of course cut the plants back if you wish. It will set back growth and flowering for at least a season or two, perhaps more. And you don't want to cut back into significant diameter wood.

Put wood chips over the root zones to protect against trampling and compaction of the soil. You may also have to wrap the basal stems to keep the bark from being scraped off by boots.