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It will not hurt the plant to cut these off. You can remove them at any time, unless you want to use the seeds. Then you should wait until the seed pods are dry before harvesting them.

It is probably not termites, but rather borers, specifically roundheaded borers. They can get into wisteria and cause damage like you describe. This article has more information:
http://www.ipm.ucdavis.edu/PMG/GARDEN/PLANTS/INVERT/roundheadbore.html

But, if you still want to kill the wisteria, cut it back and paint the fresh cuts with undiluted Round-Up. The plant will "suck" this back into the root system and that will work to kill the roots. Repeat this with any suckers that appear in the next few months.

The cut roots are likely the issue, especially if the tap root was cut or damaged. The plant is trying to reduce its size to something the roots can still support. I would recommend a heavy pruning of the wisteria vine so that it better matches the current root system. Also, follow the steps in this article for treating transplant shock. It is currently going through something similar to transplant shock:
https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm

Wisteria are amazingly resistant plants, so I have no doubt they will bounce back. It takes them a year or two to get established before they really take off and bloom. If you foresee the weed whacker continuing to be a problem, I would recommend making small collars for them out of flexible plumbing pipe to keep the weed whacker from doing further damage.

Have you checked how hot the structure gets? If it is in direct light, especially afternoon light, it could be heating to the point where it is cooking the plant on the trellis.

Another possibility would be that the trellis is not stable and shifts in windy weather. This would cause it to rub against the vines and scrape off the bark of the vine, which would kill it above the scrapes.