If the heliocentric model is simpler and more elegant than the geocentric model, then Occam’s Razor suggests we should use the simpler model unless there’s a compelling reason otherwise.

Agreed

We do know the distances to the other planets and stars. We use radar echo to figure out how far away the planets are (because we know the current speed of light) and we can measure stellar distances through parallax. Planetary mass, orbital velocity, and distance from the sun can also be calculated by tracking their motion across the sky and applying Keppler’s laws. Space probe data also helps confirm.

We presume to know because those things are influenced by the medium through which they are traveling.

Parallax of other stars has been successful one (1) time, and that was at 0.00001 of a degree.