However the slow loss of power was a hint for me that it could be the same. We know that the Finns can make ter'angreal, so I suspect they could have told the AS millenia ago how to make angreal in exchange for something 'small'.
Another mystery is how the actually managed to hold Lanfear and Moiraine. Rand managed to hold them off with a simple sword of Fire. My thoughts are that perhaps they lost consciousness, or the whole place on that side went nuclear and everyone was blown up and woke up either in jail or dead.
I think it's as simple as they were unconscious when they ended up in 'Finn-land and the 'Finns simply kept them in a s fugue state while they absorbed the ability from their bodies. The means by which they forced them to embrace the Power is the bigger question since Moiraine, at least, was quite aware of what was happening to her.
Didn't Moiraine say something to the effect of the 'Finns had her use the angreal because it offered them more saidar? They just left it on her wrist, which, IIRC Mat bargained for her return with all of her belongings ... I readily admit though, that this is not one of the books I've read as in depth as the Jordan books so I might be misremembering.
It's not a well described Talent. She can copy ter'angreal but I don't recall her using the Power to do so. It's probably like puzzle building or people who can do Rubik's cubes.
I find it interesting that the Companion explains Elayne's ability as more personal than simply a Talent. Her ability to copy and reverse engineer ter'angreal seems more about the way her mind works than anything to specifically do with the Power:
FROM THE COMPANION ENTRY ON ELAYNE
Yet Rand refers to her ability as a Talent ... Perhaps there is more to her Talent than we know.
I think RJ ended up explaining that Aginor overdrew his ability and Rand was stronger because Aginor had just spent 3,000+ years locked near the edge of the bore and his ability had atrophied without him realizing it. But you are correct, I think most comments/ OP feats from the first 3 books are somewhat suspect as it's clear the series evolved into much more once commercial success called for expansion on the series. Much like Rand and Ishamael's sky-duel being explained as "a miracle of the creator" 
