Solar Eclipses for dummies: Step 1 - moon equatorial orbit around a planet without axial tilt
May, or may not.
No.
Q1: A formula: yes, a simple formula: no.
Q2: Not for each point on Earth. This is e.g. due to different distance quotients.
Q3: Depends on distances, sizes, angular velocities, position on Earth.
Q4: Yes, but it's different for each point, not just by latitude. Even at the equator, there may exist points with, and points without totality. That's since the shadow of the Moon isn't cylindrical, but a cone. And because the Earth isn't a plane perpendicular to the Sun - Moon axis. And the distance Moon - Sun is varying due to its orbit around Earth.