The Moon has long days and nights compared to Earth and there’s no atmosphere to even out temperature differences so the climate is pretty extreme. Like Earth though, the temperature varies from place, getting colder near the poles.
Near the equator on the Moon about midday the surface temperature is about 110 deg C, at midnight near the poles, it can drop to about minus 200 deg C.
Planets around other stars are very far away and very dim compared therir stars, so we cannot usually see them. Instead we use indirect methods to discover them. Astronomers find planets around other stars by observing the effects the planet has on the star. For example as it orbits its star a planet’s gravity will tug on the star so it appear to wobble (very slightly, it’s very difficult to see), or the planet will block part of the star’s light it the planet moves in front of the star so the star appears to get dimmer (again this is really hard to observe)