- Merana was shoved aside because none of them recognized the Hall. Verin and Alanna were not really part of the rebels, and Kiruna & Bera left before the Hall was even selected and had no real attachment to their authority. The point in that was that Merana had no recognized authority. Rafela or one of the women stronger than Merana could have shoved her aside (IRRC, she was at the bottom of the Salidar sisters selected by Bera and Kiruna to go on to Cairhien with them, suggesting that Seonid & Masuri were stronger as well. In fact I think Merana actually stated that a couple of her group were equal to Kiruna & Bera. The problem was the lack of official authority, because Kiruna & Bera were there at the beginning, and deep down inside, knew the Hall was not legit, and just a pack of cranks in a village, however good their cause might be. And they had also been officially deputized, in a manner of speaking, being sent out by the authorized council to find Rand. No one overrode any authority, they just filled what they saw as a vacuum of legitimate authority.
- Rand would not know a woman's strength in the least, and the Salidar group had up to date information about his lack of women who could discern strength. They sent their embassy to Caemlyn, where he was known to be WITHOUT a sister or even a Wise One.
- That was not an issue of authority. They had authority based on their strength, because there was no official authority in place. Once they came up with the idea of making fake authority, the strongest sisters maneuvered to grab it because they knew that formal authority would trump their strength.

There is no indication that she was selected based on strength or anything other than qualifications.

Because Elaida was the one who befriended Morgase! RtDB.