Three observers, one instant, one sky. Move them wherever you like and compare what each of them has overhead.
Drag a marker to move its observer. The coloured disc is that observer's horizon plane: the half of the sky they can see.
Same observers, same star catalogue, same renderer. Only the geometry changes: the ground becomes the azimuthal equidistant map centred on the North Pole, with Antarctica stretched into a rim of ice, and the sky becomes a firmament that carries the stars and turns above the disc in one piece. Move an observer here and it moves up there too.
There is no single flat-earth model. This is the common one: monopole disc, solid firmament carrying the stars. The Flat Earth Society rejects a physical dome outright and puts the vault down to light curving upward. No south celestial pole is marked because this model has none: declination -90° is smeared around the entire rim of the disc, with no point to converge on.
Nothing can set on a dome above a plane: every point of the firmament stays at a positive altitude for every observer. The model answers "perspective", a body vanishing below an apparent elevation of one arcminute. For stars 5000 km up that rule only bites at 17 million kilometres, 859 times the radius of the disc, so it has nowhere to apply. The panels below therefore show the geometry as it stands, whole firmament in view at all times. Day and night are drawn as a bounded pool of light, which is what proponents put in place of a terminator the model cannot produce. The Milky Way is left out: the stars follow the model's own rule, but nobody on that side says where the galaxy sits on the firmament, so drawing it there would mean inventing a claim.
The three horizon planes are parallel: on flat ground the horizon never tilts. Everything else follows from that.