Nowhere Man/WMG

Veil's wife was NEVER his wife, but grew to have feelings for him

 * She was just a plant, whom manage to have SOME feelings for him

The Government knows about the organization, and are fighting a losing covert war with them

 * The Marathon episode all but confirmed this. The organization eventually creeped in to the US government with their agents, thus for all intents and purposes compromised the government's ability to investigate them. By the time Thom got involved the US Gov had all but lost.

The organization is a subsidary of Rossum and a forerunner to the Dollhouse. Spoilers below

 * Think about it. We know the organization uses Fake Memories and have the tecnology to completely reprogram a subject's personality. We know Thomas Veil's "name" is Gemini. Sounds like the codename for an active right? They're fake memory tech was even used to make whoever Gemini is think that he's Thomas Veil. He was told in the finale that the whole thing was just an experiment to test the limits of his belief. We know Rossum has a lot of power and influence so it wouldn't be that surprising.

The same group that burned Michael Weston is responsible for Veil's erasure

 * The group that burned Michael Weston was originally another branch of the organization that burned Veil.