What happens if the vampire is knocked unconscious and then the resident tells another person to bring them inside?
The another person can freely drag the vampire into the house. The vampire is not entering the house, he is being entered into it which is a different act.
Yes, but it wouldn't have the effect you expected because the people still living on those homes have not invited them in.
Invitations are not associative and not transitive. If I invite John to my enter house, that doesn't allow James to "infer" that he's also invited, nor does it allow John to invite James into my house.