I'm positing a non-planetary world but within Euclidean space. This world has things that resemble mountains (but probably not plate tectonics). Elevation varies considerably, but on average it is perfectly flat as far as any inhabitant could tell. If they were to do the various experiments Flat-Earthers should do, they'd discover that their world wasn't spherical.
Inhabitants experience "falling" which gives approximately 1G of acceleration. But if the extent of the world is infinite, true gravity would have collapsed this into some sort of singularity, so it's probably not gravity as we know it.
There are no stars in the sky, or any typical astronomical bodies. This causes a deep black darkness which is only broken up by a strange phenomenon... appearing out of the eastern sky is a giant fireball that streaks across the sky to the west. It is visible for a long time as a faint bright dot (the inhabitants call these stars) before it appears directly overhead (or close enough to it) to provide a period of several hours with "daylight" and warmth. When it is overhead it will appear far larger, but as soon as it does it starts receding into the western sky where it is visible as a "star" once more.
If this world has periodic day/night cycles of approximately 24 hours, can anything be inferred about the size of the "sun" or its altitude? For how long will the eastern and western stars be visible in the night sky before they're too faint to perceive with human eyes (assuming no obstructing mountains/elevation on the horizon)? How far north/south can one travel before it is perpetual night or they freeze to death? Are future suns visible in the east during daylight (and past suns in the west)? How fast do these suns travel? What color are they, can they be roughly the color of our own sun?
How much can any of these things vary without the people on the surface being wiped out (either by a sun flying too low/slow and frying them, or their world freezing, etc)?