You can hang the film in a U shape, if necessary. Sometimes it helps to put a half or full twist in so that the bottom isn't just flat, or clip a hanger clip onto one side at the bottom. Otherwise the water can pool some in the U.
We have one cat, and I have a dedicated darkroom space, but the cat doesn't visit the darkroom so fur hasn't been a problem, FWIW. I guess she isn't a fan of photography.