The old woman is a medium, and they are trying to find out who is in the house. Nicole Kidman et al are becoming disturbed by the interference from these people, and so they think there are ghosts in the house, little realising that it's them. They can't leave the house because of all the fog (but really it's cause they are dead), and her husband returns for a short while, even though he's dead too. When the little girl looks like the old woman it's because the barrier between our world and theirs has been momentarily broken.
I can't really remember much about the servants, apart from they're dead, but they know they're dead, and they know the family is also dead. That's why they want to keep the children away from the gravestones, in case they realise.