When I stepped further I fall out of the Library.

additionally the librarian can't make heads or tails of what is going on, this was after 30ish minutes of checking.

Shortly before this I found a Hex that did not have any bookshelves, when I stepped in I fell through the floor.  

All three of these scenarios you've described make me strongly believe you jumped down the hole in the middle of one room and landed on one of the floors below. Is that true? If so, then all of the things you see are expected. Trying to get to a room without using the stairs will "break" the library. 

The reason why I'm not loading the floors if you jump down the center is because the simulation very quickly wouldn't be able to keep up loading with the speed at which you'll be falling. You could keep falling into the abyss forever and just have the whole thing lag like crazy. I also think jumping into the hole is currently a very convenient way to quit the application on desktop versions. 

I guess I could have it load the floors if you fall up to two stories, but quit if you fall through more. However, I don't really see a huge benefit in this feature and I currently also don't plan to release an update anytime soon.

That being said, if this happens even after you've only taken the stairs then that's most definitely a bug, so let me know if that's the case.