Do snowy owls eat fish

No, they are too big to digest.

ANS2:Yes, they do but they prefer lemmings. See the link for the National Geographic article that this quote came from:

A snowy owl's preferred meal is lemmings-many lemmings. An adult may eat more than 1,600 lemmings a year, or three to five every day. The birds supplement their diet with rabbits, rodents, birds, and fish.