Is it permissible for two people to share two different types of sacrificial animals (a sheep and one-seventh of a cow), and divide their price and meat equally, such that each pays half of the total cost and takes half of the meat from each sacrifice?

The described co-sacrifice (udhiyah) is not permissible for either of you, neither for sheep nor for cattle. For sheep, co-sacrificing is not permissible at all; a sheep is only sufficient for one person and their household. As for one-seventh of a cow, it is only sufficient for one person, and co-sacrificing is not permissible if one's share is less than one-seventh.