How may a vow (nathr) be distributed, and is it permissible to slaughter it (the vow offering) at home or elsewhere?

If you intend for the sacrifice to be a sheep, a cow, or a camel, then what you intended is binding upon you, and it is required that it meets the age of the sacrifice. If you intended to slaughter an unspecified sheep, then you may slaughter in its place something equivalent to it or better than it. It is permissible to slaughter the animal anywhere, inside or outside the house, and there is no evidence to prohibit slaughtering inside the house.