I saw the trailer, there is this little girl. I was wondering if you can possess her or any other children in the world if they even exist at all.

Man, I don't see anymore childrens in the game. And kill or posess them? don't think so, in videogames that thnigs are very censured, except maybe Bioshock.

Pretty sure is the only child in the game and she is a narrative valuable NPC so no you cannot kill her or possess her.