No, Beavers do not eat fish. Most of the beaver's diet is made up of tree bark and cambium, the soft tissue that grow under the bark of a tree. They especially like the bark of willow, maple, birch,...
None, they're strictly plant eaters. They eat the bark and leaves of trees mostly.
Since they are a small fish (max size 8 inches) they are eaten by many of the larger predatory species like salmon and trout.
Because large fish have to eat whatever they can get.
Yes, they also eat other dead crayfish, dead plant matter, live plant matter, and even smaller live crayfish