Either I missed an episode, or this new lady in Doctor Who is, well, new. My original thought was that she was the TARDIS (materialized as a human) but now I believe she’s the future Clara.
My proof is this; the Doctor, near the end of the episode, tells Clara that he is not her boyfriend. Later, my predicted future Clara, refers to the Doctor as her boyfriend.
I also believe the answer to “Did the Doctor push him or did he jump?” is that it was neither. The Doctor (when he disappeared and Clara thought he had left her the second time, when there was nothing but a square on the ground where the TARDIS had been) travelled back in time and saved the Cyborg (apologies I cannot remember his name), then later brought him to the future Clara.