Eve was a member of a species destroyed during the Last Great Time War. They had certain elemental powers, including psychic abilities and time alteration.
Eve was a humanoid child, with red skin, eyes and hair. She had large, extended ears.
Eve's race could read timelines and control objects from a distance. They also had the ability to possess and control humans. A juvenile of the species could be strong enough to manipulate objects for a short while but would eventually be exhausted by the effort. Their powers were at least partially linked to their technology, as demonstrated by Eve's Ship absorbing excess energy from her after she tried to control too many people and machines. (TV: The Mad Woman in the Attic)
Eve's race was destroyed in a war between two great races, the Time Lords and the Daleks. (TV: Sarah Jane's Alien Files episode 2) Their ability to read the timelines had made them a target for elimination. It was not stated which side attempted the genocide, though it is presumed to be the Daleks, as Eve said they were exterminated. Eve was smuggled onto a ship by her parents, who sent her to Earth as an evacuee. Her ship crash landed on a beach. Harry Sowersby, the caretaker of a nearby funfair, found Eve. Under orders of Ship, he kept her in the haunted house away from civilisation until Ship rebooted.
When the funfair was closed down, Eve became lonely so she kidnapped and possessed four homeless people to play with her in the fair. When Samuel Lloyd came to the fair, his mind was read by Ship, who found information about Rani Chandra and her friends. Ship believed they could help and made Samuel contact Rani and bring her to the fair. When Rani arrived to investigate the funfair on her own, she stumbled across Eve. She persuaded Eve to leave the haunted mine, but Eve tried to control too many people and rides and began to burn herself out through an excess of energy. Helped to the crash site at the beach by Sarah Jane's companions and Harry, her energies were absorbed by Ship and her health was restored.