1) I think she's the little sister of Kylo Ren. Luke was a Jedi and so was not likely going to have kids if he was true to the Jedi covenant. Makes movies 2 and 3 more compelling if it is a sibling rivalry versus cousin rivalry. I also think that you'll likely see Kylo turn good at the end of 3.

2) that was unclear to me too

3 & 4) JJ Abrams said that the Knights of Ren were not Sith. My guess is that they are followers of Kylo when he massacred the Jedi padawans. He created an order that was neither Sith nor Jedi. Then he got picked up by the Supreme Chancellor, who my guess is Palpatine's master who conquered death, came back from death after Palpatine's treachery (resulting in his wounds and deformations in the movie), and then took control of the empire when Palpatine and Vader died.

Probably wrong, but my 2c.