That's the 'Full Moon'.
Not exactly. The lighted side of the moon as seen from Earth is that part that is not shadowed by the Earth.
New moon.
That would be Third Quarter.
"First Quarter", roughly 7.4 days after the New Moon.
That's "First Quarter", roughly 7.5 days after New Moon.
That's called the "Third Quarter" phase. It occurs about 22 days after the New Moon.
"gibbous"
half moon
You can not see the new moon
The Moon phase when only a sliver of light can be seen is known as the crescent phase. It occurs in the second phase, known as the Waxing Crescent Moon, and in the last phase, known as the Waning Crescent Moon.
First Quarter and/or Third Quarter.
That's the one called "First Quarter", taking place about 7.4 days after the New Moon.