If I level up on my character (full level, not a skill), does the game automatically save?
While I can't speak for Xbox 360 (although it's likely the same or similar), the system settings menu in the PlayStation 3 and PC versions has four options:
And, even considering the possibility that they don't enumerate all possible autosave opportunities in the settings, it did not save after I leveled up: no message in the upper-left hand corner, no lag associated with autosaving, and the autosave functionality kicked in on schedule at the 15 minute mark later on.
I then confirmed this by loading my last auto save, which was before I leveled up.
So level up has no effect on autosaving.