1 - An AI character could absolutely live in the Library's digital space! It's not a terribly high-tech digital space, but it's possible!

2 - Any character with any kind of control over technology, AIs included, can get up to technological-poltergeist shenanigans if they're inclined to. They won't be able to flicker the lights, because the Library isn't so high tech that it's a Smart Space, but they can flicker monitors and blare music all they want!