Yes, as the moon is orbiting the Earth, the moon rises and sets at different times each day or night. All of the waxing moon phases (i.e. waxing crescent, first quarter, waxing gibbous) rise during the daytime before sunset.
No, the full moon rises at sunset. The 3rd quarter Moon rises about midnight.
Yes, that is the meaning of moonrise.
it rises at sunset and sets at sunrise
Any moon apart from the new moon can be seen in the night sky, although the only moon phase that is above the horizon the entire night is the full moon. The gibbous phases either rise just before sunset or set after sunrise, the quarter phases either rise or set at midnight and the crescent phases either rise shortly before sunrise or set shortly before sunset.
there is no moon rise
The waning crescent moon is the phase of the moon right before sunrise, it is seen in the eastern sky just before sunrise.
Does the moon rise in the east?
Since the new moon is between the Sun and the Earth, it will always rise at sunrise, whatever the time of sunrise is at any particular location.
it rises at sunset and sets at sunrise
Any moon apart from the new moon can be seen in the night sky, although the only moon phase that is above the horizon the entire night is the full moon. The gibbous phases either rise just before sunset or set after sunrise, the quarter phases either rise or set at midnight and the crescent phases either rise shortly before sunrise or set shortly before sunset.
there is no moon rise
The waning crescent moon is the phase of the moon right before sunrise, it is seen in the eastern sky just before sunrise.
Does the moon rise in the east?
Because a sunrise or sunset are local phenomena. You cannot see such things if you are not in that location. The sunrise on the earth refers to when the sun appears over the local horizon or disappears below it for sunset. Where you are affects affects what you see astronomically speaking. On the moon you would see the local sunrise and sunset for your location on the moon.
Moonrise and moonset are caused by the rotation of the Earth, same as sunrise and sunset. As the Earth rotates, the sides of the Earth facing the moon changes, making the moon appear to rise up and then sink below the horizon.
Sunrise
The moon rises from the eastern horizon, just like every other astronomical body. The time of rising varies smoothly throughout the lunar month. It can be anytime from a minute after sunrise to a minute before sunrise. On the average, the moon rises about 50 minutes later every night (or day) than it rose the night (or day) before.
sunrise surprise
Sunrise (and moonrise) is when the leading edge of the sun just breaks the horizon, and sunset is when the trailing edge of the sun just sinks below the horizon. Observations may differ slightly from calculated times, since air conditions will effect the bending of the light