Answer:
I lose my head in the morning and regain back it at night.
I don't live within a house nor do I live without. Most will use me when they come in and again when they go out.
What word begins and ends with an E, but only has one letter?
Adored by few, feared and hated by many. Mistress of the entire universal reason, master in the art of numbers. Some may have solved many of my mysteries, but there are still many of them to find. What am I?
My seas have no water, my mountains have no rock, and my land has no grass. What am I?
What is lighter than what it is made of?