OK, here's what I think, for those who are interested. We did some research on minks, and discovered that: they eat muskrats, and chickens, of course...they also eat their prey on the spot and consume most of it. They also sometimes climb, though not good at it. And we already knew that they are native to Ohio and that we have them in our woods, because we have seen their tracks in the snow in the winter, especially around the pond, of course. And, I also learned that they have a big territory, and they move around a lot, so they wouldn't necessarily stay in the same area more than a day or so. So that explains, the nocturnal squirrel the kids saw (probably); the total and on the spot consumption of the muskrat and our hen, the neck cracking (they kill by breaking the neck), and only one hen being killed. Of course, it isn't conclusive, but it makes sense. And there may be more than one predator involved here, but, as I said, there were some similarities in those two attacks that I had not seen before in other predator attacks. In the case of our hen I don't think anything had time to drag the rest away (like mice) because it was a very fresh kill, and it was during the morning. Mink are related to Fishers and are native to Ohio, whereas Fishers are not native to Ohio. (I know that doesn't mean they can't be here though) The claw marks and broken tree branches we still can't explain, other than maybe a very large cat or raccoon maybe got far enough out on the branch to break it? We are still interested in getting a game camera or two.
