If the Earth is represented as a 1cm ball, how far away would the moon be in cm?

Easy - ratio of distance of moon divided by diameter of Earth = 3.8*10^8/1.275*10^7 = 30. So if Earth diameter were just 1cm, the distance to moon would be 30cm.

In the 1cm Earth model, how far away would the sun be? The sun is 400 times distance of the moon so that is 120m.