Interesting questions and very much a personal decision. I've eaten an injured chicken before. It had a bad leg and the thigh and drumstick on that side were discolored so I discarded those but ate the rest.
I've never eaten a chicken killed by a predator, but I've had very few of those. But predators can have some pretty nasty bacteria on their teeth or claws from the meat they otherwise eat. That's what can make certain animal bites or scratches dangerous. I might consider it if the only damage was to the head but probably not. Another possible issue is that it's never a convenient time to butcher anyway when I find them so I've ever really been faced with that decision.
I've never eaten a chicken that died from disease or medical reasons. Again, very few opportunities but I don't keep mine around for old age. Theoretically very few if any chicken diseases are not going to transfer to humans. If you cook them well you're going to disinfect them anyway, the only time of risk might be before you cook them and I think that risk is really small.
It's probably a bad analogy but predators pick off a lot of diseased prey because they can be easier to catch, or they scavenge recently dead animals. Their immune system is probably a lot stronger than ours since they do it often, that's why i think it is a bad analogy.
I grew up in the ridges of Appalachia many decades ago. I had relatives that lived much as people in the mountains lived in the 1800's, subsistence. They lived off of what they could get from the land. I have absolutely no doubt if one of their chickens had died from disease they would have eaten it. But I don't have to live like that and maybe I'm not that tough. So while in theory there is probably nothing wrong with eating a chicken that died from a disease I wouldn't do it because of what I call my personal YUK! factor.