Force user =/= Jedi. Jedi is a title just like Padawan, or Sith or Darth or Grand Moff. Luke is literally the last Jedi. He tried training more, but Ben/Kylo murdered the turders out of them all. Just because he trains Rey to control her power and not be a giant dick to everyone, that doesn't necessarily make her a Jedi. Unless Luke trains her in the way of the Jedi, she's just a force user.
I don't know if they'll kill Luke or not, I suspect they will considering how cyclical all of the other movies have been thus far, but I'm thinking that Rey's training will be very different from a Jedi's training and this new method of using the force will be proven in episode 9 against Snoke (who is most likely a very old school Sith).