I had the exact same thing happen to me last summer, as far as the heads with no chicken. It was strange....every day, I would run across a new head in a different raea of the yard, but under trees and bushes. An owl was picking off my banty chicks like it was nothing. I ended up losing all five and it was heartbreaking. At that time, I posted and the concensus blamed an owl...which I HAVE seen in our tall pines in the yard. So, with almost absolute certainty, I would bet you have an owl. As far as your cat goes, I dont really know. I sure hope you find her though-I know what it's like to have a beloved kitty disappear! Good luck!