This is indeed confusing. They should be thoroughly thrashed with a wet noodle. And they should stop. Altitude is the complement of the zenith distance. Zenith distance is the angle from the zenith.
Vertical angle is something different.
Yes, but these names can be very troublesome indeed. It certainly seems worth the trouble to me. It also seems that an ephemeris server to run it, together with a team of computors and updaters of orbits, would make a great deal of sense. People with special requirements could be authorized to make particularly deep or lengthy searches. If such a server existed, perhaps NASA and the RSA could be persuaded to update it directly, particularly for shuttle maneuvers and Mir reboosts.