SPOILERS (Don't read if you haven't seen the movie)

> Why does the Emperor tell Darth that Darth killed Padame if he knows that Darth didn't directly kill her?

IMO, Palpatine had no intention of saving Padme. He offered an explanation, so he wouldn't turn on his new master. Full of deception, he is. At least indirectly, of course, Vader is responsible.

>I seem to recall that the Emperor told Darth that he has two kids in episode IV, is this revealed in ep. IV?
>

IIRC, the Emperor informs Vader about Luke in Episode V. Vader learns about Leia from Luke in Episode VI.