I have a theory on Rey that is not as simple as "She is Luke's daughter" and ties the OT with the PT.
What if when Luke went into self imposed exile and no longer used the force, the force itself made another woman pregnant like it did with Anakin.
Anakin never knew he could use the force until Qui Gon showed him, and Obi Wan taught him.
Maybe Rey never knew she could use the force too, when she was near Anakin's lightsaber, the resonance of something that was used by another person created by the force drew her to it, and started activating her hidden talents, but they were still largely dormant until she was mind probed by Anakin's own grandson.
There were clues in that scene that instead of probing her mind, she had in fact probed his, and learned everything of the force from him, then later in the fight, when she called the sabre to her hand, everything suddenly snapped into place.
Sure, he was trained, but only his mother was a Jedi, if Rey is truly a child of the force, then she would be as strong in it as Anakin was before he started losing his limbs.
That is why she bested him so easily, because she is the new chosen one.
R2's low power mode could only be turned off by proximity to a Skywalker, and Rey might not be one by birth, but by the will of the force.