You need to decide what you want to accomplish. If things can be changed, would you want this job anyway? If you do want this job (assuming it can be saved/fixed) then what is it that needs to be changed?
Your point 6 nails it - as I see it you need to go to the CEO and say that while your title is "manager", your "team" is actually going to and taking direction from the CEO. As a result, you say, you are unable to do the job.
Now you need to make the decision as to what you want, or you can simply leave it up to them. Choose:
* Say that you require the authority as well as the responsibilities, so your team must only take direction from you, except in exceptional circumstances which must then be confirmed by you;
* Say that since you are not given the authority of a manager then you require that you return to being a member of the team;
* Give them the choice between the above two options, and that whatever is agreed must include written confirmation of the separation of duties.
But you must decide what it is you want to achieve. Yes, it would be a PITA to relocate again, but as it stands you will be miserable, in danger of being "let go" regardless, and have no control. If you do take control of your own destiny, at least you will have some control!
You have the title of manager. That doesn't just mean that you tell your team what to do, it also means that you must manage your relationship with your manager - the CEO. Perhaps even start by saying that you are keen to make a success of your position, you need their assistance and guidance, and that to do your job properly you must be given the authority. To phrase it like that means they demonstrate power by giving you the control you need.
FWIW. As I say, random advice from a random stranger on the internet.