>>1015476Watering them will be especially important while they are making the berries. In the spring, before the new shoots come up, you can cut out all the dry brown dead canes that fruited the year before. On the rare occasion that I do this, I use a tree/brush trimmer style like this so I can reach in a good bit into the bramble bush. Keep in mind that these "bypass" ones sometimes warp a little and jam when trying to trim something as a steep angle. A perpendicular cut is best with this. The "anvil" style are easier to use for high angle cuts without jamming.
The wild blackberry canes are much thinner than the cultivated varieties, so you shouldn't have trouble cutting them with either style tool. You may want to wait until the buds come out so you know 100% which canes to cut out.
>>1015484Usually thicker than a pencil. It isn't just cutworms, there's also Oxidus and Isopods that readily chew up the stems, though isopods are the worst and most pervasive. The latter are normally what has cut something off instead of an actual cutworm.
>>1015490Cover with buckets, bedsheets, plastic trash bags, etc. Just use sticks to prop up the stuff to keep it from touching the leaves. Is that 20C or 20F? 20C shouldn't be a problem at all. 20F plus a clear sky = frost.