It is getting to be breeding season for birds, at least in the northern hemisphere (it does not say in your profile where you live, if you put that in, it makes it easier for people to help you) so I'll assume you are in the northern hemisphere like I am. The hooting could be the owl trying to find territory or a mate. Although owls don't normally hunt in the day time, like most predators they are opportunistic. If there is some really great and easy meal to be had, they might take it either in the early morning or later in the afternoon. I would say it's not real likely, but I have lived long enough to realize that even things that are really unlikely sometimes happen. You might consider getting some netting or something to put over your run. One strand of fishing line might not help much to deter a hawk if it's really hungry, and then the owl would not be a problem either.