If it was in a cat's mouth, regardless of paint, Google "Avian rehabilitation" with your state and you'll get a list of rehabbers. Bring the bird there.

It's much too young to be leaving the nest and the bald spots are either undeveloped feathers, or nest mates may have plucked a few feathers. I suggest soaking some dry dog food in water and setting it out for the parent bird....this will make feeding the chick easier and also provide a nutritional diet for the chick. If the Maya will eat it, you can also offer canned dog food. You've done a great job and the parent is definitely dedicated! I would try raising the chick higher in the basket by placing mats, cardboard or papers under it's bedding. Raise him enough so it's not so difficult for the hen to feed, yet keep the sides tall enough so he can't easily fall out. If you can keep cats and dogs away it has a good chance of survival.

It could be that the bluebirds are trying to take over the nest. I haven't heard of them eating baby birds, but chickadee nests get invaded often. What is the diameter of the hole? Eastern bluebirds typically need a 1.5" opening to get in & out of a nest box. Chickadees can go as smal as 1 & 1/8". Many people put hole restrictors on after Dees have laid their 1st egg so that other birds can't get in. You may also want to monitor (open) the box to make sure babies are ok. Do you see the parents feeding the babies? Hope it all works out!

For the birds, though, whenever I comb my cats, I pull the fur off the brush and put it outside. One time I found a bird nest and it was lined with my cat's fur. :)