Again, I'm discussing morality, not law. US law is contradictory on this point: it gives a homeowner property rights extending downward to the core of the earth, but does not give property rights extending upward into the heavens.
Yes it does. The owner of a property also has subsurface (mineral) rights and air rights unless they have been sold off or "severed".
An exception on air rights has been made for high flying aircraft.