I'd highly recommend that you get the book. It's the best treatment of an astrographical area that I've ever seen, and it covers your questions.
In brief, the reason that the Gateway Domain was created was politically motivated, in the event that the Imperium decided to expand in that direction. It is one of the few frontiers left where such expansion could occur. Doesn't mean that the territory belongs to the Imperium, but that the Imperial territory in this region is administered by someone that serves the Emperor in exchange for being given such a high level of authority.
Hope that helps,
Flynn