Azura has the ability to basically see into the future, so how does she do this? There was the Nerevarine Prophecy and she is credited with warning her followers of the impending eruption of Red Mountain before the Red Year happened. Is it actually foresight of some kind or does she only know of these things before they happen because she is partially responsible for them happening?

Well, she's a god. For starters.

This is also the most useless contribution to this topic. I'm sorry :[