Nelavaire is not particularly strong in the One Power. Her level of strength is described by "The Wheel of Time Companion" as 28(16) which is a middle level in Aes Sedai hierarchy. With this level of strength she is unable to open alone a suitable gateway to Travel.
"The Wheel of Time Companion" confirms her Cairhienin origin.
She was born with the spark and was allowed to enroll at thriteen because it was beginning to manifest itself.
She remained loyal to the White Tower during the split following Siuan Sanche's deposing. She is one of the sisters who was captured after the Battle of Dumai's Wells. She has now bonded the Asha'man Naeff.
She probably fought in the Last Battle alongside Naeff.