Edward and Alice

Edward must have met her after he was already married. I think they just became close during the grief counseling group and fell in love, but he's to moral a man to act on it. I don't think there's any complex backstory. It's just a detail and establishes character.

You raise an excellent point, the screenplay is deliberately vague on this issue.

Its one of the reasons that I speculated that we are meant to consider that Edward Walker might have been Lucius Hunter's father.