That phase is called the third quarter or it could be called a waning half moon.
half moon
crescent moon
All of the Moon's lighted side is visible during the full moon.
That's the 'Full Moon'.
"Waxing" is the term used when the Moon's illuminated part is growing in size, while "waning" means that the lighted part is decreasing. "Gibbous" means more than half, but not full. So "waxing gibbous" is the phase of the Moon between the first quarter and the full moon.
You can not see the new moon
No
The moon phase "waning gibbous" appears after the moon phase "full moon".It becomes the "last quarter" or "third quarter" when the lighted part is exactly 50%of the side facing the Earth.
The lighted half of the moon is always facing the sun. The entire dark half of the moon is facing earth at the time of "New Moon".
First Quarter and/or Third Quarter.
This is the first quarter phase. The moon looks half lit, half in shadow, but you actually can only see one quarter of the moons surface at this point (during a full moon, you would only be able to see half of the moons surface - the half that faces us).
That would be Third Quarter.