You really need to get her to see a vet as soon as you can. She is very sick. Here is a directory of vets who see chickens - http://www.poultrydvm.com/poultry-vets.php
No, it looks like one of your birds was probably bleeding at some point. You may be hard to see where the wound is because it's dried up. I'd check their feet, as it looks like it may have been a foot wound.
I am not sure that headshaking is a sign of mites. Here is an infographic which might be a bit better to help you identify whether you actually have mites or not, and what species they might be, as that is the most important step to getting rid of them -...
Raccoons are pretty good at getting latches open. But I believe it is something like as long as they are 3 steps to them that they can't get in. Here is an infographic though which better helps answer that question for you -...
Hemm, maybe this infographic about how to spot creepy crawlers on your chickens might help. I do not think it looks like mites though - http://www.poultrydvm.com/featured-infographic/identifying-common-ectoparasites-of-backyard-poultry
You're gonna need to put wire across the top of it. Here is a good infographic which has details - http://www.poultrydvm.com/featured-infographic/tips-for-protecting-poultry-from-predators
Oh wow, that is pretty bad. If it were me I would take her to see a vet. But here is a case story about what sort of things are done for chickens who experienced predator attacks by dogs - http://www.poultrydvm.com/cases/goldie
I would recommend predator proofing your run/coop. Cuz the predators just keep coming, and chickens have lots of predators. Here is an infographic about predator proofing - http://www.poultrydvm.com/featured-infographic/tips-for-protecting-poultry-from-predators
Here is some info and case stories about scissors beak, which should help answer some of your questions - http://www.poultrydvm.com/condition/scissors-beak
Well, I think the same logic would apply to other natural disasters as well - http://www.poultrydvm.com/featured-infographic/chickens-hurricane-infographic