Answer:
My first keeps time, my second spends time, my whole tells time.
What runs around all day. Then lies under the bed. With its tongue hanging out?
Something wholly unreal, yet seems real to I. Think my friend, tell me where does it lie?
Neither bought nor sold but more valuable than gold. It is built but not by hand. What is it?
What goes up when the rain comes down?
You use it between your head and your toes, the more it works the thinner it grows.