Personally I'd like to see Rey with a blue double-bladed saber if for no other reason than to do something different and uniquely her's. Making it out of both the remain's of Anakin's old hilt and her staff just seems poetic as well as both metaphorically and thematically fitting.
How or where she might have gotten a second kyber from isn't that important. Presumably the next movie will feature a much more significant time jump, which leaves plenty of possibilities open. Hell, we still don't know for sure where Luke got the kyber for his green saber between tESB & RotJ!
Yes, but is it Jedi training? If I get trained by a Jedi Force Ghost does it count?
Have tongue in cheek. Kind of serious.
Well it clearly worked, so I guess so!
On a more serious note: remember the quote
"luminous beings are we, not this crude matter."
What fans call a "force ghost" isn't really a ghost, just basically that "luminous being" which has shed it's crude matter and become one with the cosmic force without loosing it's individuality. So Qui-Gon is still Qui-Gon just as Yoda is still Yoda. Plus of course "Jedi" is a doctrine. An idea. Doesn't really matter where the information comes from, be it a hand written text, a wall carving, an ancient holocron, or indeed the disembodied consciousness of a Jedi Master that has returned from the netherworld of the cosmic force. It's still the Jedi philosophy.
That part that interests me the most though is the larger implication that Yoda and by extension, Obi-Wan & Luke receiving this rare training was a decision possibly made by the force itself. In the TCW episodes Qui-Gon straight up says that both he and Yoda have been "chosen" because dark times are ahead and the light must be preserved. It's not happenstance; something very powerful very deliberately set these events in motion.
There's a larger purpose to all that knowledge and experience being preserved and what else but to aid the new generation of Jedi, both to learn the ways of the force and to learn from the mistakes of the Jedi Order of old. Even Anakin being a part of that group makes sense as he has *by far* the most experience with the temptation of the dark side and what it costs.