Loial decides Rand is ta'veren not because he can recognize ta'veren but because he knows of the ta'veren effect.  He had to hear Rand's story first to realize it.

Egewene and Elayne may not be Ta'veren but they might have a special talent. If i remember correctly in the glossary of one the books (yes, i actually read the glossary), it stated that there was a talent similar to the affects of Ta'veren but in a much lesser extent. And since both Egewene and Elayne can channel it is not unlikely that they could have this talent (at least thats what i always assumed, besides why else would RJ put that in the glossary?).

The talent for reproducing the effects of a ta'veren in a limited area is a function of the Power. A learnt aspect. Neither of the girls can do it.

 

Rands Ta'veren twist had Egwene raised as Amyrlin if you ask me

 

Thats impossible, he was in Cairhein, and the decision was made in Salidar--his ta'maral'ailen is large, but its not that large.

 

Yes, the Aes Sedai were reacting to him in choosing Egwene--and part of that is reacting to the effects his ta'verenism has on the world, but they were not themselves under its influence.

 

Let me put it this way--within his ta'maral'ailen people do things that they had a one in ten million chance of doing normally. Outside his web, they are not influenced--but they still have to react to these people doing these extremely unlikely things.

 

The Aes Sedai did not raise Egwene Amyrlin because they were under the chance-manipulating effects of a ta'veren, they did it because they chose to in the face of the world as it was, and that facts that that presented to them. Amongst those facts were the facts of Rand's existence, but equally important were the deadlock between Lelaine and Romanda and Suian's manipulations to see Egwene in power.