I adored Rebecca, and Jamaica Inn (and Don't Look Now).
Thought it very clever that, yes, we don't know the girl's name and that the book is named after someone who is dead. Very powerful stuff. Still get the chills remembering Anna Massey as Mrs Danvers, staring down from an upstairs window. (an ancient TV adaptation)
I really liked the 1940s Hitchcock film. Very atmospheric!
To answer Q2, most definitely. Every part of her life is taken over by Rebecca to the point where (if my memory serves me correctly) she even ends up wearing her ballgown, even if that was the result of an evil ruse by Mrs Danvers. The fact that the second wife isn't given a first name is a constant reminder to the reader of just how completely the first Mrs De Winter, despite being dead, seems to dominate her life.
I'm afraid I can't answer Q1 right now as it will involve too much soul-searching.