I just played the MQ of Oblivion. And never played the oldest TES (Arena, Daggerfall, etc), so i don't know if in any of this games there is the answer to my next question. Neither have i read the biography of our Seventh Septim found in Skyrim.

This guy knew way too much for his own good. "Dreams" he called them, but i don't believe it. The Nerevarine, his death, the role of the unknown prisoner that became the Champion of Cyrodiil and Hero of Kvatch, the role of his illegitimate son Martin. I'm guessing that he read some elder scrolls from the White Gold Tower. How?
Thoughts?
Sources?

I think it was pretty much stated that he knew about the Nerevarine from an Elder Scroll. Can't remember where, though.

I think it's the Amulet of Kings that gives him insight into things, and I could see that playing through his dreams. Though for the Elder Scrolls themselves, he has Moth Priests in the tower to read them.

Dragons are sensitive to the flow of time, as Paarthurnax explains to the LDB. So it's very possible that a dragonborn could have prophetic visions regarding his own future. Uriel himself says that his visions don't reach beyond his death. Uriel also was trapped in Oblivion for a long time, and I think his biography states that the visions started after or during that time.
So being a human dragon who was trapped in Oblivion and usually sits in the middle of a Tower representing entire Mundus, with that Towers stone around your neck, which also happens to contain the souls of every dragonborn emperor before you, can do things to a human being.

I don't recall that exact quote, but the decoded package to Caius mentions he had faith in the prophecy and had consulted experts.

something else that helps and lends to this theory is that of few people or things the amulet of kings can tell you what happened during a dragon break according to http://www.imperial-library.info/content/where-were-you-when-dragon-broke so who knows what else it can do