1) The library fairies have always been a part of the library, as far as Dawn remembers. The invisible fairies that teleport lost items to the research center are mostly the ones from the kingdoms. All fairies are capable of teleporting themselves and items much larger their size around, so they've chosen tasks that suit them around the city and segments. Some are even helping to make the teleport stones at the center.

2) Dawn shakes her head because she has no theories on that. Harrison might, but he doesn't like talking about anything without actual evidence so it's probably better not to ask, honestly.