Is there rain, snow, thunder and wind on the moon like the earth? Is there always no day and night on the moon?

That's not true. There is no air and water on the moon, it is a vacuum environment, and there are no weather phenomena such as rain, snow, thunder and wind.

The moon rotates, so day and night alternate on the moon.

Just because the rotation period of the moon is the same as that of period of revolution, it is a period of the first month of the lunar calendar, that is, 29.5306 days. In this cycle, the surface of the moon is half night and half day.

Terminator line on the moon