Do the rulings on dogs, in terms of the prohibition of raising them except out of necessity, and their impurity upon touching and so forth, apply to what results from mating dogs with wolves?

That which is born from a dog takes the ruling of a dog. Thus, a dog and a pig, and whatever results from them, take their respective rulings; they are impure. It is not permissible to acquire or raise that which is born from dogs, unless it is for hunting, guarding, livestock, or similar purposes.