During night on the Moon is there Earth light and Earth phases?

Yes, there are Earth phases, viewing from the Moon. Full earths, half earths, quarter earths, waning and waxing earths. The easiest way to visualize this is, imagine the earth is still, one half of the Earth facing the sun, the other half away from the sun, so you have half the Earth is light, half is dark, now, imagine you're on the moon orbiting the Earth every 28 days. When you're over the sunny half of the Earth (night on your part of the Moon) the Earth is full. When you're over the dark side of the Earth (day on your part of the Moon), the Earth is new. As the moon takes 28 days to orbit the earth, like the moon in our sky, every 28 days would complete one cycle.

What's different is the Earth wouldn't move in the night sky. It would actually go back and forth a bit, but it would stay in the same general area, every day, every year, every century, because the Moon is tidally locked to the Earth, but apart from not moving, it would be similar to the Lunar cycles.

Another difference is that you could observe the Earth's rotation. Here's a pretty good video on what it would look like. 28 days squeezed into about 1 minute.

https://www.youtube.com/watch?v=-HgHEO0DUig

I would imagine the Earth looks quite bright from the point of view of the Moon, and I'd guess the pictures don't really do it justice, but that's just a guess. I've never seen it for myself. I'm also not sure it would be pitch black and not visible as a "New Earth" either. I remember reading that you can see stars from the moon even during the day, that's because there's no atmosphere to diffract the light so you could probably see the Earth even at new earth too. We can see the new moon from Earth sometimes, so I would think a "new earth" would be visible but dark.

Here's a discussion on being able to see the new moon. I would think, seeing a new earth from the moon would be even easier.

Short discussion: http://scienceline.ucsb.edu/getkey.php?key=26

Long discussion: http://physics.stackexchange.com/questions/1907/why-can-we-see-the-new-moon-at-night