Answer:
I look at you, you look at me, I raise my right, you raise your left.
Inside a great blue castle lives a shy young maid. She blushes in the morning and comes not out at night.
This thing runs but cannot walk, sometimes sings but never talks. Lacks arms, has hands; lacks a head but has a face.
What has roots as nobody sees, is taller than trees. Up, up it goes, and yet never grows?
No matter how little or how much you use me, you change me every month.
The strangest creature you'll ever find: Two eyes in front and many many more behind.