1. Yes, they actually do. This is why when you feed a raw diet, you have to include bone and lots of vitamins, to make up for the 'rest' of the animal. (With birds, they usually rip most of them off first, but if your cat is eating it whole, I'm sure some feathers get swallowed as well.)
2. As long as the bone is raw (cooked bones are a no-no) your kitty should be fine. Is it Possible for him to choke? Yes, but it seems he has enough experience eating animals already, he should be fine.
The dog may be wonderful prose, but only the cat is poetry. - French Proverb