Answer:
I have an eye but I cannot see. What am I?
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?
The time between daylight and darkness when blood drinkers like to come out
What is harder to catch the faster you run?
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.
I have feet on my head