The Aelfinn and Eelfinn were probably discovered sometime in the transitioning century/ies from the 1st Age to the age known as the AoL. It was probably accidental, as a result of learning and studying Portal Stones, which most of us know predate the AoL.

 

More than likely the ToG is the central doorway to the actual 'otherworld' of both of the enigmatic beings. But, probably in the AoL, Aes Sedai made doorways to both of them, ter'angreals that gave users a limited time, etc., bargaining time, with which they could learn more, and such.

 

The Tower of Ghenjei is more than likely made from Aes Sedai work, possibly in conjunction with human workmen as well as the Aelfinn and Eelfinn. Only the 3 novels coming up will tell us in the future.

 

 

About gateways, the books seem to indicate that the world of the Aelfinn & Eelfinn does not have any.