I'm the guy that works on the moons, so I'm putting my Ideas up here.

The Week: (and the corresponding moons)
Day 1: Black Moon (Death, Necro, and Zombie Magic)
Day 2: Red Moon (Fire Magic)
Day 3: Clear Moon (Wind Magic)
Day 4: Yellow Moon (Movement, Teleportation, and Telekinesis Magic)
Day 5: White Moon (Life, and Rez* Magic)
Day 6: Blue Moon (Water Magic)
Day 7: Green Moon (Earth Magic)
Day 8: Reflective Moon (Phsykic, Mind Reading, and Enchanting Magic)

*a note on rez magic, it drains your own life force to keep the other person alive.

I put the offensive spell categories in the first half of the week, and there opposites exactly 4 days away. The more defensive spells make up the second half of the week. The idea is that any school of magic you use, is more powerful on the day of the week that has that corresponding moon, and is weaker, when the opposite moon is up. For Ex., fire spells are more powerful when the Red moon is out, and less powerful when the Blue moon is out. Otherwise, it's pretty much normal.

Names:

Because it doesn't sound profesionall if you call each of the moons by their colors all the time, I came up with some names. Feel free to offer different suggestions for them.
Black: Decessus
White: Vita
Red: Ignus
Blue: Unda
Clear: Aer
Green: Viridis
Yellow: Traetus
Reflective: Consulo

More on looks and inhabitants next time.