Answer:
Tear me off and scratch my head what once red is now black.
A man shaves several times a day, yet he still has a beard. Who is this man?
The faster you run, the harder it is to catch me. What am I?
I have a head and a tail but my eyes can never see my tail.
Lovely and round I shine with pale light grown in the darkness a lady's delight.
Give it food and it will live, give it water and it will die.