Min Farshaw also had sex with Rand and in fact got to spend the most time with him. I can't remember which book this started in. In Winter's Heart, the latest book as of my writing, Elayne Trakand also got to sleep with him, but only because Min forced him to go see her, knowing that he was in love with all three of them.
More details on one matter: Aviendha struggled against her love for Rand because she was good friends with Elayne, who loved him first and so he "belonged to her." But the two eventually became First Sisters, which means they can't let a man come between them and therefore both have to marry him or neither. Elayne also considers herself a First Sister to Min, although they have not taken the vows, and is currently trying to get Min and Aviendha to become First Sisters also.
And yes, the Wise Ones require that all women who can channel become Wise Ones also (though women who can't channel can also choose to). Men who can channel, on the other hand, are expected to go into the Blight and kill as many Shadowspawn as possible before they get killed.