I always believed that Enclave scientists simply brought samples of the FEV virus with them when they fled to Raven Rock from Navarro. Its never explained (of course) in game, so we are left to our own speculations.
By virtue of Fallout 3, Navarro has already been given many more troops than we saw in Fallout 2. So I think we can reasonably assume that the base has (due to Fallout 3) been "upgraded," probably similar to Adams Air Force Base in terms of importance and capabilities.
With that in mind, I don't think its unreasonable to believe that Enclave scientists were perhaps testing samples of the virus there. Autumn Sr. after all, was a lead scientist at the base, so we can assume a strong(er) scientific force.
I don't think we can rule out the involvement of Vault 87's virus either however. I also believe that the issue with the current modified virus's lack of a airborne form may have been caused by the different strains.
Truthfully, I can't. Just as I can't come up with a suitable explanation as to why Autumn does a double-take during the purifier incident. It's one of those mysteries of Fallout 3.
I believe it may have been used as a way to calm the populace from any reports of Vertibird or advance scouting activity. We don't really know for how long Eden has been operating the radio, so it may not have been much before the LW left the vault.
The object being of course, something of a "Tokyo Rose" senario. Disarm the populace with your words and prevent undo hostilities. If a revolt were to occur against the Brotherhood spurred on by the radio then its just icing on the cake.
Its not a good explanation really, but its the one I generally go with. Otherwise there's little reason for its existence, even by Autumn's standards.
I of course, don't rule it out as Eden's "ego." He has no reason to pretend to be the President. He is the President. Why would he want to pretend to a bunch of people he wants to dispose of anyway? There's plenty of soldiers who are staunchly loyal to him within his actual faction.
Or they simply lack the equipment to do so.