Is there also a way to auto-tick Remember playback position by the fact that something is in the audiobook or podcast folder?
This should already happen automatically.
How to I change the default audiobook folder?
I'd like to move E:/music/Musicbee/Audiobooks/ to E:/books_audio/
Do you have auto-organize enabled (in library preferences)? In that case, just change the auto-organize setting for audiobooks. Otherwise, you can move them by selecting the files, right clicking and choosing "Send To > Folder (Move) > Move to Organized Folder."