The Citadel wasn't a source of power, it was a mechanism. The Crucible was the power source; as was explicitly stated.
Regarding the Catalyst: that was just a code name given to the final component by the Protheans (translated into English, obviously), the AI probably only knew of the name because it learned it via TIM. It pretty clear it doesn't have a name for itself because it doesn't need one, it just need it's stated purpose: "I bring order to chaos."
As for it knowing of the Crucible; it explicitly says that it first learned of the concept several cycles ago and believed it had been eradicated. It even admitted it underestimated the organics. Probably one of the main reasons it was unaware that the Protheans had it was that their methods of data storage and retrieval was uniquely tied to their physiology and not something that could be read or understood by a machine.
Indeed this is one of the main plot point in ME1. The whole reason Sovereign was using Saren they way it did was because it needed an organic interface. Just like they needed Shiala to acquire the cipher from the Thorian and Benezia to get the relay co-ordinates from the rachni.