SPOILERS: Second Story Questions
I'm not sure why the doctor got killed in the second story. Did she kill him? If so, why?
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Incredibly late reply on such a dead board, but the singular theme of the movie is that love transcends life and death and soul mates never part.
The first story seems pretty straight forward but at the very end we find out that Aoi and the main character have apparently been in love since they were children, but for some reason Aoi commits suicide (or just possibly dies by accident) so mom binds her soul to the intern after death.
The second story is a little confusing, but again, the twist isn't fully revealed until the very end. Asako falls in love with the doctor after he helps her finally let go of her guilt and she dies. So her spirit leads the doctor to that road where he's hit by a car and joins her in the after life. That's why at the end the doctor hears her voice saying "I love you."