I think they might be eating eachothers feathers because they lack the proper nutrition in their diet or she might be pulling out her feathers to relive heself because she has mites.
I think you have a black leghorn. Notice how chickens that have white earlobes lay white eggs and chickens that lay brown eggs have red earlobes. It is usual for blood to be on the eggs when they first start laying. The eggs also might be long or have a very thin shell or not have a shell at all.
If you want to catch a coon I recommend buying a live trap. Put it were you think the coon travels most frequently and you peanut butter for bait. This method has worked for my several times when a raccoon was getting into my sweet corn.