Question

What is the Castor's distance from the sun? What is the diameter of the castor star? How far away from the earth is it? How far away is the castor star from the moon?

Answer 1

By
https://en.wikipedia.org/wiki/Castor_(star):

The Castor star is about 51 light years from the solar system. This is about 500 (european) billions of km (`500xx10^12 km)`!. The value is so humungusly big that it is irrelevant if it's from the Sun, the Earth or the Moon.

It's diameter is 2.4 times the one of the Sun: about 1.6 million km.