I would avoid using the SIL because on her form, she will indicate how she knows you. If she puts SIL, she won't count. And if HO find that connection through marriage, it might be a bit suspect (especially if she has the same surname as you!).
As far as I know, they did not contact my referees. But I'm pretty sure they checked to be sure they were of good character and that at least one of them had a valid British passport.
Yes, use the name on her passport. You'll have to give the passport number and her name, and they'll look it up... you want them to find match.
My ceremony was 14 December, and I did JCAP (is that still offered?)... my passport arrived on 24 December.