I dont think that was the policeman who she saw through the police car window - I think he was standing outside but I think she saw a hallucination of another, similar looking man - I think the guy she saw had a thick moustache whereas copper didn't? I may be wrong though. I think there may be sexual abuse in Paula's childhood maybe.
I don't think James knew Paula and her brother from their childhood.
I may be completely wrong but did anyone else think James' Mum looked exactly like Paula - as in maybe CGI/ SFX?
To the people saying it's unrealistic - I don't think it's meant to be taken so literally, it's not a Broadchurch/ Midsummer murder mystery I think it's meant to be much darker and full of motifs/ metaphors/ symbols etc (can't remember the proper term!!). I think there may be a more supernatural and ambiguous ending.
That's how I saw it anyway