> Only for 2 weeks per month

Why?

Lunar night is 2 weeks, so you get earth visible 50% of the time from any point on the lunar surface... and earth will be the biggest thing in the sky

The Moon is locked in rotation with its revolution. A location on the Moon that has the Earth above the horizon will always have the Earth above the horizon.

Lunar night means that the Sun has set - but the Earth remains in the sky in the same position.

The moon doesn't spin relative to earth so if you can see the earth in the sky, it will always be in the sky. If you watch the phases of the moon, you can easily see that the darkness is just covering the same face that we always see. A moon base would always have line of sight to earth but would be in darkness half the time. Great for comms, not as great for solar power.

Er.... No. Earth is either visible 100% or 0% of the time, the Moon is tidally locked