See, I don't really get the interest in this stuff. It would be fairly irrelevant if not for the Tower's asinine hierarchy. Being the most powerful channeler is like having the most powerful gun. It can help a lot, but the skill of the user, and his tactical acumen and ability to take advantage of the situation far outweighs that other factor. Since she's dead, and her influence seemed to come from her Talent and her selection as adviser or Keeper.

Not remotely. Channelers live a lot longer than that naturally, while Aes Sedai get cut short anyway. I recall no quote saying that age is connected to strength (only to the degree of slowing, which can be anything from superficial details like wrinkles to health and body functions). We KNOW the curtailed aging is due to the Oath Rods being used in the AoL to punish wrongdoers, in which case the idea that the strength of the user would affect the duration would be counter-indicated by that use. If stronger channelers lived longer, and lasted longer under the binders, then punishment would be less for them. The AoL Aes Sedai made the binder and would have known about that effect, so they cannot even be said to be applying the binder in ignorance the way that the White Tower is. For them to be using it as a preventative measure that is less effective on potentially more dangerous channelers, or to be using it to mete out unequal justice both speak equally poorly of their moral or ethical character.

Irrelevant. Elaida targeted Morgase because of her Foretelling. Gitara served a completely different woman, of a completely different House. There is no indication that Tigraine's mother had any way of knowing the strength of a sister, and that is not the sort of thing Aes Sedai would let normal people base judgment on. According to their SOPs with the normal people, the Tower is the Tower and sisters are sisters, and it's not the place of outsiders to judge one against the other. Also, there is little or no indication that the Tower or any sisters are involved in the selection of the Queen of Andor's adviser. Elaida played up to Morgase to get her job; Elayne chose Nynaeve, instead of applying to Egwene to appoint someone; Alteima asked if Morgase had replaced Elaida, not if she had received a replacement. Siuan remonstrated with Elayne for causing Morgase's disenchantment, citing her lack of an adviser, a situation that was plainly not Siuan's choice but Morgase's. The choice is the Queen's, and no normal queen would have the ability to discern her adviser's strength.

Secondly, you are overlooking the most obvious criterion Elaida and Gitara have in common: Foretellings! Which do YOU think would be a factor in choosing someone to give advice, regardless of who does the picking? The ability to lift a few more pounds with the Power, or the ability to obtain special information?