Is there any way to delete the Personal (Web) notebook and create new notebooks from OneNote for iOS? I've tried deleting from the web interface, but it only recreates it immediately. I'd love to be able to click the new note icon in the middle of the taskbar but it defaults to this Unfiled Notes section. I'd prefer to be able to choose which notebook it goes into it. Any advice on this workflow?

Also, is there a way to create a new notebook in the iOS app or am I relegated t the web app?
Yeah I have had the same issue and for the same reason.

I think the OneNote app is pretty limited in that area and you are dependent on the web interface alot.

I am not sure if you also use Windows desktop app - but they seem to sync together. 

There is an app called MobileNoter that also syncs with OneNote, only the PC version though. 

In Short there are and you will need to think of some work arounds unless you are able to live with the limitations of the app.

Guess MS really wants you to buy the software on the PC:-)