A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Tony Oz
Date: 2019 Oct 14, 10:35 -0700
Dear David, I can answer only to your #3 question: the common name (the "Horizontal Parallax") is a misnomer, it should be the "parallax in altitude of the body observed at the horizon", i.e. it is just the maximum positional error - when the body's (Moon's) altitude is ~zero.
Hope that helps.