Did Luke know the "Chosen One" prophecy?

Question

When Anakin becomes Darth Vader, Yoda and Obi Wan conclude that the prophecy didn't happen. Besides Yoda and Obi Wan wants Darth Vader to be dead. They even expect Luke to kill him. But when Luke knows that Darth Vader is his father, he wanted his father to be redeemed than to be killed. At the Death Star II, Darth Vader ceased to exist and Anakin Skywalker is resurrected by saving his son from the Emperor. When the right time comes for Vader to be redeemed,

Does Luke know that his father, Anakin is the Chosen one? Did he know that Anakin was supposed to bring balance to the force?

Answer 1

  There is no definitive answer, but Luke could have heard about prophecy from various people or sources. First, Obi Wan or Yoda (as force ghosts) could have told him before or after Anakin's death (after is more likely). Second, Bail Organa could have known, because he was after all heavily involved with Jedi. From him, his adoptive daughter Leia could find out and tell her brother (Leia definitely didn't know Vader was her real father, but she could have known about prophecy). Third, Darth Sidious of course knew about prophecy, and could have left some written trail, holocron or something like that. Fourth, Luke could obtain info on his own, investigating Jedi lore. Finally, Darth Maul heard about Chosen One prophecy (probably from Sidious) . He didn't knew identity or anything else useful, but theoretically he could pass on his knowledge to someone (Ezra Bridger perhaps ? ) and this could finally reach Luke .

  All of this implies that there is very slim chance that Luke knew his father is Chosen One before events on Death Star 2. But he could have known various bits and pieces before events transpired and whole truth after the deed was done.

Answer 2

Pure speculation, as there is no exact canon info:

Before RotJ - No

Only two people could have told Luke this "Chosen One" theory correctly: Obi-Wan and Yoda.

Given the reluctance Obi-Wan accepts that Luke knows the identity of his father, it is unlikely that he or Yoda would disclose the rest to Luke. Also, Obi-Wan doubted that Anakin was the Chosen One any longer after his downfall and conversion to the Dark Side in RotS. He possibly thought that the whole "Chosen One" business was a mistake.

^{Revenge of the Sith Novellization: Chapter 20}

Obi-Wan: “You were the chosen one! It was said you would destroy the Sith, not join them. It was you who would bring balance to the Force, not leave it in darkness. You were my brother, Anakin,” said Obi-Wan Kenobi. “I loved you, but I could not save you.”

Thus it is unlikely he would tell this story to Luke, neither he had time while he was alive.

It is unlikely that Yoda told Luke the "Chosen One" theory, as it clearly brings more confusion. Luke already had to make a hard decision to confront his father. If he knows that Vader is the one to restore the balance, it becomes too confusing and demotivating, and could lead Luke to a decision not to fight Vader.

Out-of-the-universe: the "Chosen One" theory might not have been invented yet, possibly another ret-con of the prequels.

After RotJ - quite possible

We do not know how and when Luke communicated with the Force Ghosts of Yoda, Obi-Wan, and Anakin. They could possibly tell him of the concept.