Can you shoot that bird down? I've never tried, since I only ever notice it inside of cities.
Oddly enough, I just tried this a few minutes ago. I timed my shot so it would connect with a hawk along its flight path and...
Spoiler Wait for it...
Spoiler The bird simply disappeared from existence

1/ Is there a way to keep track of the books you have in your house as I am building a collection but its a pain going through them every time I have new ones to make sure I do not have duplicates.
This one's easy, just grab a pad of paper and write down the name of a book when you attain it. Before taking one, check with your list to be sure it's not already on there. If you're a PC user, I suggest convincing someone to make a mod that adds an "(obtained)" tag to any duplicate instances of books that have previously been in your inventory.