The only requirement for becoming a novice, set by Egwene when she was Amyrlin was that you only had to test true and you could become a novice, no matter your nationality, age or previous family life.

Since everyone who can channel can become Novice the requirements for Accepted needs a slight clarification. To be raised to accepted is to not only come and learn how to use the One power or study at the tower, but to set on a path to become Aes Sedai. A girl or woman unwilling to resign a normal family life for the time of being Aes Sedai will not be raised unless it is asked for by the Amyrlin. Other then that the old requirements stand that is. A novice who has learned to control the source enough to not harm herself or others can be called to the testing. If she turns down the call she can do so three times, but at the third time she has to leave the tower. Not turning the calling down means that she will meet her fears in the three arches ter'angreal, one for her past, one for her present, and one for her future. If she wants to break any time during this test she will also be sent from the tower and if she breaks afterwards (the first few weeks involving severe pressure on her) she will also be sent away.

To become Aes Sedai the Accepted has to be mature enough to handle the responsibility. She may have no channeling blocks and she has to pass a channeling test under extreme pressure. To this test she is only called once and if she fails or turns down the call she will be sent away.

Sent away doesn't mean being sent away for good. A Novice who has finished her education and left the tower can join the Kin, there is no reason any longer to feel alone and unable to work as a channeler in the world.