And I would be just fine with anything within that limitation. No one is fighting over rulership of the island and its surrounding lands, and I have no doubt that either Egwene or Elaida (assuming either was thinking rationally) would concede to the other absolute queenship over those lands in exchange for being acknowledged as the Amyrlin with her authority limited to Aes Sedai and the Tower and its grounds. Of course, that would not stop Elaida from trying to immediately win back those lands and title from Queen Egwene (though I believe Egwene would leave Queen Elaida alone). Rulership of Tar Valon is just a sideline for the Tower and the Amyrlin, while it is the raison d'etre of a real government of a nation. The difference between the two is like the difference between a homeowner and a business that owns the premises out of which it is based. For the latter, property ownership is a sideline and a means to an end, while for the former, it is the end in itself. If the Tar Valon and all the lands the Tower currently rules were suddenly sunk beneath an inland sea and all the non-channeling inhabitants transported to another nation, the Aes Sedai would regard it as a nuisance or an encumbrance, but they would not say the Tower was gone, or that they were no longer organized or anything. Tar Valon means no more to the Tower than a corporate headquarters means to a company. Both still exist without the physical location. A nation of people can still exist if they no longer have land (such as the Tinkers or Jews), but they are not a state any longer.

No, she does not, since the Tower law does not acknowledge this, anymore than a mail clerk has the right to hire a group of mercenaries, seize the executive suite and call himself the CEO.

Do the names, Delana, Moria & Sheriam mean anything to you? In any event, Egwene was not raised by Sitters. She was raised by a pack of cranks in a village. If her election was legitimate, then Rand could choose out 21 sisters sworn to him, call them the Hall of the Tower, and have them raise Alivia as Amyrlin. She would be EVEN MORE legitimate than Egwene, since her Hall truly represented all the Ajahs. No more than a third of the sisters selected Egwene's Hall, so they cannot claim to truly represent the Tower.

Then Luke Skywalker and Han Solo were not rebels, either, since they were not there at the beginning, and were no doubt on the census as citizens of the Galactic Empire. As soon as she accepted the rebellion, Egwene became a rebel. True, she did not have a choice about accepting the summons, as an Accepted could not disobey sisters (though we then have the issue of her behavior in Cairhien - even a rebel Accepted should not have been evading the sisters with the embassy. If they wanted to drag her back to Elaida, it is her duty to go every bit as much as it was to obey a summons of sisters to Salidar), but once they claimed she was the Amyrlin, she is not constrained from returning to the fold. The minute she opened that first gateway in her study, she was a rebel, because she did not go to the real Tower as her duty required.

Elaida is legitimate because the Blue were legally excluded from the sitting that elected her. Absolutely no one, include Anaiya, who was cited as the most anti-Elaida rebel, denied her legitimacy. Can you really think that Anaiya would miss the fact that Elaida had no Blues in the sitting where she was raised if that detail had any significance? She could not call Elaida the Amyrlin unless she believed it to be true. You could argue that the Sitters in the Tower, including the one who had proposed Siuan in the first place, and admits she would not have supported deposing her, were just ignoring the technicality. You could argue that Elaida was in denial when she claimed that she got the Amyrlin Seat by making use of a loophole in the law, and that she actually broke it. You could argue that Cadsuane does not know all the facts when she states that Elaida is the rightful Amyrlin. But you cannot argue that even the Salidar rebels would blind themselves to any lawful argument against her rule!