Faolain is dark of complexion and has a round face and dark curly hair.
Strength and Abilities
By Aes Sedai standards she is quite strong in the One Power, equalling Melaine, who is stronger than most Aes Sedai. She is likely on the same level as the likes of Anaiya Carel and Myrelle Berengari.
This is almost confirmed by the Wheel of Time Companion, which lists her strength at level 17(5), that is enough to open suitable gateways for Traveling.
She never seemed to like anything or anyone. Although she is unpleasant and can be a bully, she has a strong sense of justice - as evidenced by her choice of the Blue Ajah. She also disapproved of the manner in which Siuan was deposed, despite her personal dislike for her and her disapproval fo Siuan's actions as Amyrlin. And even though she disliked Egwene, she disapproved of how other Aes Sedai did not properly respect her for being the Amyrlin.
In the White Tower
She is seen earlier in the books as an Accepted and often serves as a messenger, sending for Egwene and Nynaeve al'Meara (whom she seems very cold towards) to the Amyrlin and greeting Min Farshaw at the gates of Tar Valon when she arrives the second time.
She is allied with the Salidar Aes Sedai, and did not resist being led to Salidar by the Aes Sedai that fled. She did not approve of the manner in which Siuan Sanche was deposed but she also blamed her for having broken the White Tower, and so she did not resist being taken from the White Tower by fleeing Aes Sedai. However, she did harass Siuan as she felt she should have been deposed - legally and properly - for her actions.
Raised to Aes Sedai
When Elayne Trakand and Nynaeve arrive in Salidar, she is there to "greet" them and takes Nicola Treehill and Areina Nermasiv to be tested for channeling ability. She is still hostile towards Nynaeve.
While in Salidar she had been raised to something higher than an Accepted but not quite an Aes Sedai, alongside Theodrin Dabei. Both had been deemed ready to take the test, but simply could not as the ter'angreal needed was in the Tower. When Egwene al'Vere is raised as Amyrlin her first decree is to raise Faolain, Theodrin, Nynaeve and Elayne to a full fledged Aes Sedai. Egwene did this so Nynaeve and Elayne could be free to search for the Bowl of Winds in Ebou Dar; Theodrin and Faolain were included as they were closer to being raised Aes Sedai.
She pledges to Egwene an oath of fealty and will be one of the few Aes Sedai Egwene can trust. Although Theodrin is stronger in the Power, Faolain takes the lead. Because Faolain hasn't used the Oath Rod other Aes Sedai still do not regard her as a full sister. At that time she doesn't like Egwene and made that clear but she also dislikes how the sisters treated Egwene as if she is not the Amyrlin Seat.
She also has mixed feelings about being raised by decree; she is grateful but at the same time dislikes how she is treated by other Aes Sedai.
Lelaine Akashi has decided to take her under her wing and uses her as an attendant. She is actually being used as a spy to report all activities about Lelaine to Egwene and Siuan. Faolain dislikes being placed under Lelaine's wing - it would mean being treated like an Accepted who had to be watched closely- but was grateful for the chance to do something useful.
She goes missing when Lelaine finds out about her spying for Egwene. Lelaine presses Faolain hard for information she may know and then places her in confinement.
She is part of the delegation sent to the Black Tower, where she chooses a Soldier Asha'man as Warder under Lyrelle Arienwin's instruction. Some Aes Sedai bonded two, but Lyrelle told Faolain to only take one. Like the rest of the party from the Black Tower, it can be assumed Faolain fought in the Last Battle, though it is not specified alongside whom. Lacking any other information, it is presumed she survived.
Min has had a viewing of Faolain that "good things" will come to her. This is additional evidence that she survived the Last Battle.
After Reunification, as in the case of Nynaeve, it can be assumed that also Faolain and Theodrin Dabei had to be tested in the Oval ring and swore on the Oath Rod before being recognised as full sisters by the others.