I had an owl go into a shelter where some were sleeping in the run and drag one out. It tore the head off. The the chickens sleeping in that shelter never did again. I've also had a hawk take a chicken in the middle of the day, again going for the head. Many predators go for the head first, it's a fast easy way to kill a chicken. Even if they actually eat other parts the kill is often at the head. Neither the hawk nor the owl carried the chicken away. They ate on the spot.
I've seen practically every predator there is out hunting in the middle of the day. Some are more likely to come out at night but "more likely" does not mean 100% of each and every time, always and without a doubt forever. I was very surprised when I saw possum sitting on my compost pile having a snack at 1:00 in the after noon on a bright sunny day.
It is very possible you could have two or more different predators. When I set out to trap a raccoon I often get a possum or two first. Over three nights I may get three raccoons.
It is possible the predator was frightened away after the kill but before it could eat.
Some people go years without a predator problem, then without doing anything differently, a predator attacks. You never know how good your predator protection really is until it is tested. You may be tested immediately, you may go years before a certain predator comes by.
There are a lot of myths and misunderstandings about predators. They can't be as bad for everyone as I've probably made it sound. a lot of us are able to keep chicken even free range without huge problems. But they can strike anywhere at any time.
That last attack sounds like it could have been a hawk. There are a few other thing it could have been. For those night attacks an owl, fox, coyote, or bobcat immediately come to mind since they were drug outside but it could have been something else too.
I wish you luck. These things are often kind of hard. You need to know what it is so you know how to set a trap.
