This is my view on the matter at hand. Biasness of course, but seriously, who isn't bias (admins excluded of course;))
1. No, I believe that the AW do not control Omicron 74. The point was made quite clear I feel on the forums at the time when the AW lost its official status that they also lost the rights to a system that came with it.
2. You have the right to patrol these places and enforce small laws specific to AW (such as restriction of traffiking certain materials, stopping fights between two sides, etc), I think. However, restricting base access isn't within that, as that would be using power of the Zone of Influence, which I believe the AW lost when they lost their officiality.
Think of it like this. An independant Rheinland Military unofficial clan starts up, and begins enforcing RM law. All is good, until they try to bar docking to people who aren't on the RM official register. Then, the RM bans them from Rheinland space.
Okay, not the best analogy, but you get the point...
3. IF AW still controlled Omicron 74, it would most probably be official and would have rights to make laws as the ruling faction in the area, as it did in the past. And hence, if that were the case, my order/request would indeed be illegal. But that isn't the case. I took in all the facts and consulted the relevant people before making that post. Also, why would Corsairs be hostile to Zoners? They are supposed to tolerate each other, but the current reasons and my percieved alignment of AW displace that theory, as the AW, in my opinion, prefer to keep our right side fronts open to our heartland.
I. I maintain as I have done for some time that the affiliation of Zoner tag and ID does not fit. I would possibly look at Mercenary, Bounty Hunter or Freelancer IDs with the Zoner tag if you wish to keep your current role the same.
II. If you are also thinking about changing your affiliation, then I would recommend you pick something more friendly towards the Outcasts. If you are also thinking about changing your aims and objectives, then you might want to advance the story to do with the AW and mould them into something new and possibly completely different from what the AW are now.
III. From my perspective, the AW like to claim Zoner affiliation and neutrality, and yet side with the Outcasts, sometimes openly against us, while letting them through to our home system without allowing us to intercept. This lack of a buffer system worries us a lot, and there are many tactical reasons that this conflict had escalated into a war.
So, a summary of my views, picked from a chat I had with someone.
AW, being unofficial, has both the positive and negative effects of being unofficial. They don't have to follow any strict guidelines on faction management for one, as all these other unofficial ones can also do. However, being unofficial, they have no right to act under their own power to police an area. Just because you RP a group of Zoner "protectors", doesn't mean you have the right to police said territory in a way an official faction would or claim bases in the area to be your own, as well as the guard system. AW is indeed a unique case as they were official but have become unofficial. They should get used to the fact that, losing their officiality meant that they lost what power they had to do as they wished in their ZOI, which doesn't exist anymore in terms of the rules of the game. However, the AW also don't have to adhere to the strict rules that official factions have to adhere too.
EDIT: Oops, forgot the AW have their own ID. Personally, I consider that to be a Zoner ID with a different name, but it does say AW on it.