Answer:
A precious stone, as clear as diamond. Seek it out while the sun's near the horizon. Though you can walk on water with its power, try to keep it, and it'll vanish in an hour.
Although my cow is dead, I still beat her. What a racket she makes!
Runs smoother than any rhyme, loves to fall but cannot climb.
I am whole but incomplete. I have no eyes, yet I see. You can see, and see right through me. My largest part is one fourth of what I once was.
Look into my face and I'm everybody. Scratch my back and I'm nobody.
What do you purposefully put lots of in and on your body, but run away from when you encounter it outside?