Morri is not Aes Sedai. She is a Gaidin of MDD (Mahdi'in d'ma dieb), which is one of the gaidin companies. She is, however, bonded to an Aes Sedai more terrible and glorious than imagination can summon.
MDD is also the company of Raam, who was bonded here to Alex.
Yes. First guess best guess. That is exactly what it means. I would have said "hole in one" in praise, but with the Train, that's not quite accurate.
One should not speak of sacred things among the unanointed.