Yes. [Hux honestly had mixed feelings about Palpatine but he didn't really care about Palpatine being a Sith. Sith Lord or not, Palpatine had accomplished many good things in the galaxy.]

Do you know for certain it was Luke Skywalker who defeated and killed Vader then? And the Emperor at the same time?

[he was actually curious about what she knew about that, if anything. No one really knew what happened on Death Star II.]