Well it's just information, no? The only technical requirement is in storage space and processor power. They use crystals for storage so I imagine it's molecular memory, no storage isn't an issue and they have the capability to have a functioning AI (after a fashion) on the station so they're ok for processing power. As for having access to such obscure data, just look what's out there on the internet. Just the other month I was doing some family tree research and found a scan of a series of handwritten letters to and from my great grandfather concerning his army pension after he got mustard gassed. Now that's available for anyone to find, so I can see just about anything in recorded history being available in 250 years. Also, as I recall it took the computer a while to run the search, so it's not exactly at their fingertips.
Just to note this is a consistent thing in the B5 universe remember that Franklin uncovered the genocide of the Hyach-Do from a centuries old Drazi recording and the bloke who always plays psychos found out he was a mind-wiped serial killer with just a handful of keywords.
As for Delenn's belief in Kosh, leaving aside that she's a creature of faith that had a personal visit from Valen when she was a child (did Joe ever come out and admit that Sinclair went the way of Sheridan, btw?) remember that Dukat trusted the Vorlons and she implicitly trusted and Dukat, so I'm sure that's a large part of it too. Plus of course 1000 years of Minbari cultural baggage.
On top of that, before her change she got to see Kosh unsuited and was granted a vision of Valaria, which would be like a faithful Catholic receiving a visit from the Arc Angel Gabriel. Which brings us back to Mr. Sebastian; Kosh wanted to be sure of her motivations. Somehow I have a feeling that if Ulkesh was on B5 instead of Kosh that he wouldn't care why she obeyed, so long as she obeyed.
