It definitely had some flavour of the Sixth Sense, but to answer some of those points:
1) I think that the connection between the girl and the boy is this... the girl herself was something supernatural, something evil. She could sense and manipulate her physical environment (the photos/picturs she made in the hospital, the tv stuff, the burnt wall in her room). She never slept, and as such, I think part of her lived on after death. The boy has some small supernatural powers, in that he can hear her more clearly than others (like 6th sense).
2) They don\'t need to explain where the girl came from, just that her adoptive mother couldn\'t handle her influence. The girl drove her mother insane with whatever powers she had, and horses killed themselves to avoid her. Eventually, the mother got to the point where she was insane enough to just kill her daughter, because she thought she was evil.
3) Pure speculation: In the hospital the girl asks for her mother... but doesn\'t use a name. Perhaps she was stolen or kidnapped by the couple, and uses her abilities for evil because she is angry over that.
4) The main character does save herself by making a copy. What the father had said before he died made sense. The girl doesn\'t mind killing, but her goal isn\'t to kill everyone, but rather to have everyone see her suffering. So if you watch the tape, you make a copy, and in that way, eventually, everyone will see her suffering.
5) What a totally awesome movie. It\'s rare these days that hollywood comes up with a totally new script that really floors me.