Not fully illuminated moon seems to be half as bright as a full moon
Interesting thing is that the Moon before the full phase and few days after shines with more intensity than during the full Moon itself. Though only 95% are shining, to our eye it would look like during a full Moon. This strange fact makes the Moon before and after the full phase seem brighter to us.
The Earth viewed from the Moon has phases as well
Yes, Earth also has some phases. They are absolutely opposite to the chronology of lunar phases, so when it is new Moon - it is full Earth, last phase of the Moon would be the first-phase Earth. There will be a crescent Earth and gibbous Moon. The full Moon means it is the first phase of the Earth.
For Moon, the Earth is always on the same place, changing its phase time after time. However, you can not see the phase of the Earth from the far side of the Moon.
The view on Earth from the Moon makes Earth four times bigger than we see the Moon from our planet. Also, our atmosphere makes our planet shine up to 100 times brighter than the Moon shines on Earth. When Earth is in a full phase it reflects its blue and gray light on the Moon.
From our planet the shining reflected on the Moon can be observed during a crescent: the crescent form itself is illuminated by the Sun, but the rest of the round shape that is slightly visible is due to the reflection of Earth's shining. This fact was discovered by Leonardo da Vinci.
Eclipses are reversed when viewing from the moon
For us lunar eclipse is when Moon prevents us from seeing the Sun. However, for Moon eclipse happens when Earth blocks the Sun.
If the Earth fully takes the place of the Sun, from the Moon can be see only a tiny ring of sunlight and a massive dark sphere of our planet. So the Sun is like a back illumination for the Earth. The tiny ring has a reddish tincture, because it is a mix of all sunsets and sunrises that occur on the Earth at that minute. This is also the reason why the Moon dresses in red during full Moon eclipse.
When we observe the total eclipse of the Sun on Earth from the Moon, we can see how the dark shadow creeps over the continents of the Earth for a few hours. This is the shadow of the Moon, scientist called it umbra. If it is a lunar eclipse, the Moon is fully covered by Earth's shadow, because Earth is larger than the Moon. The Moon's shadow is smaller so it moves through the regions o Earth as a dark spot.