Sun and Moon

On many days, I can see the moon and the sun out at the same time, how does this work on the flat earth?

It only works in flat earth model.

In round model, there is no explanation about in a place in daylight and the other place is 180 degrees in the other side, night side of the earth has moon in the air. This is impossible in the round model.

In the flat earth model, ie, there is many models, but in some models, the earth and sun has different speeds so that sometimes you see the moon in only night and sometimes you see the sun and moon both together. It is possible if they are visible together. I could not explain very well. anyway. perhaps someone else may do it better.

I guess nowadays my energy is going down .

Does the moon cause the night in the flat earth model, or is there just a black spot?

The night is caused by the absence of sunlight.

But on a flat earth model, what is stopping the sun from shining it's light over the whole earth?

It is like a spotlight, not like a giant light bulb. The rays are more directional, I guess you would say.

If the sun is like a spotlight, then how can antarctica have 24 hours of daylight?