1. Sure, but as I said - the one thing we know for stone cold certainty about the Blades' intel on the Thalmor is, it wasn't very good. Even at the height of their power, they could neither accurately estimate the Thalmor's strength nor anticipate their moves. Esbern's speculation may be relatively well informed, but it's still speculation.
(Edit: 1a: I'm also not entirely convinced that "Loremaster" translates accurately to "chief intelligence analyst". Seems likely that "Archivist" might be a more plausible equivalent.)
2. Spot on? I thought we agreed just a few pages ago that Alduin wasn't, perceptibly, trying to destroy the world.
That's no reason to have it written down in the Embassy, unless either (a) you are over-confident in the Embassy's own security and sure it could never fall into unfriendly hands, or (b) you don't mind it falling into unfriendly hands because it's not actually true, but designed to mislead your enemies. In the former case, the lack of other written evidence in the Embassy remains unexplained. In the latter case that lack makes perfect sense, but we'd have to admit that any other evidence was also unreliable anyway so what's the point.