Obi-Wan saying that he had two pupils, Anakin Skywalker and Darth Vader: He said this in order to make the tale sound more dramatic to Luke and the audience, claiming that Darth Vader was a different pupil of his, showing that Darth Vader and Anakin Skywalker knew each other.
Obi-Wan not telling Luke his father was Vader: Okay, ever since the prequel trilogy, many mentally retarded people have been asking this for some odd reason. It was a fucking secret, they're not going to change that just because the prequel trilogy came out and not let Luke know his father was Vader.
Obi-Wan claiming he was trained by Yoda and not Qui-Gon: Why exactly would Luke need to know about Qui-Gon? He's in the snow, he's trying his best to stay alive, why would Obi-Wan say "Run to Dagobah, and find master Yoda. Oh and Qui-Gon taught me as a padawan."
The new emporer scene: Have you ever thought maybe Vader asks "how is this possible" because he's just in disbelief that a Jedi gave birth when it's against the Jedi code? I'd be surprised too.
"Jedi Rocks" being a song about Jedi after the extermination: Jabba knows about Jedi. Remember when he tells Bib that he was fooled about a Jedi mind trick? Jabba's lair is very secretive, there are absolutely no imperials there. So why not sing a song about Jedi? Now if Jedi Rocks was played in a cantina or something, that'd be a different story. Also note that even if there were stormtroopers there, they probably don't even know what Jedi are either, nor that they are supposed to be extinct. That's something only people who lived during the prequel trilogy would know.