As for the battleship thing, as far as I know, the assault was based on two types of technology. The one is what Dr. Tomsons is analyzing; a fusion of Sirian and Nomad technologies. The other is some sort of summoning device, like the kind Mason used at the end of Athena's fic/the beginning of our game. The battleships that may or may not have been present would have been wholly Nomad.
Members of The Covenant may or may not be possessed by Nomads. The thing about The Covenant is that, to a large degree, people really aren't actually members. You have your three big bosses in the organization: The Abbot, Mason, and Juan. Each of these people has access to certain factions within Sirius (The Order for Abbot, Bounty Hunters mostly for Mason and Outcasts for Juan) and usually will just send members of those groups todo their dirty work without ever really initiating them into The Covenant proper. Leastways, that's how I see it.
Hope that clears things up.