1. New moon, waxing gibbous, Full moon, and waning crescent are the main ones but there are more.
2. The revolution of the Earth is 365.25 days while the revolution of the moon is 28 days. Also, the Earth orbits the sun while the moon orbits the Earth and vaguely orbits the sun due to the orbit of the Earth.
3. Tidal waves, seasons, and the lunar cycle.
4. Moonlight is light that is reflected off the moon's surface that comes from the sun. This "lights" the moon up. Sunlight is light that comes from the sun which is made by a bunch of chemical reactions.
Good luck!