Flat Earthers, I need your help

I'm designing an open-world massive multiplayer video game in which players can discover new lands when things get too crowdy for them.
They can then expand their country on the map in all directions (northwards, southwards, eastwards, westwards), without limits.

This sounds like a description of a flat world, isn't it?

I tried the globe approach too, but it turned out to be a bit too limiting for my purposes, because the globe has a finite surface area, so I would need some way to somehow "grow" it without changing the existing map of the world too much (the cities that are already there must stay where they are and close together).
I figured that I could have "ice caps" in the far north and south where no one can go, but with time, those ice caps might recede, revealing new lands that the players could use.
But in this approach, the map could grow only in the vertical direction, so over time it would become a thin vertical strip :q
I tried to find some way to grow it sideways too, and I figured that I could use plate tectonics: the continents move apart, and the oceans between them grow, but with time the water level decreases, revealing more land that could be used by the players. So kinda like in the Growing Earth theory
But this probably wouldn't work too, because the coastline would slowly move over time, and cities that used to be by the sea (with ports etc.), would no longer have contact with the sea and would end up in the middle of the land   It also makes the cities more and more distant apart over time, which is also bad.

So I figured that a flat Earth might be the only way to go, because then I can have as much land as I need in all directions, and players taking more and more of it for themselves as they need.
But this approach has another problem that I would like to resolve:
Playing with the globe approach had a benefit that I could easily introduce day and night cycles: just rotate the planet (or the Sun around it – either way it worked). So I could easily have time zones and diurnal cycles. I could also have seasons and climate zones: hotter at the equator, colder as we move towards the poles.
But I don't see how I could have that with the flat Earth approach, and of course it would be cool to still have those features :q

So I decided to ask here, hoping that people, for whom the flat model of the world is their bread and butter, will have some answers to my questions.
I would like to know how does the Flat Earth Theory handle these five things that we observe in our world:
1. Diurnal cycle (day and night)
2. Seasons (spring, summer, fall, winter)
3. Time zones (different time of the day in different parts of the world)
4. Climate zones (different temperature ranges in different parts of the world)
5. Plate tectonics (continental drift, mountain formation, volcanic activity zones etc.)
so that I could incorporate them in some way in my game.

I would like some short and simple explanations of how these things work on the flat Earth.
Can I count on your help with these subjects?