Answer:
I am Invisible Man's drink at snack time
I am a precious stone as clear as diamond. Seek me out while the sun's near the horizon. Though you can walk on water with my power try to keep me and I'll vanish in an hour.
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?
I am not alive but I can die. What am I?
What has a head and a tail, but no body or legs?
Give it food and it will live, give it water and it will die.