Answer:
I'm a green veggie that looks like a tiny tree.
Often found in doctor's offices and pirate flags
Never ahead, ever behind, yet flying swiftly past; For a child I last forever, for adults I'm gone too fast.
Cold head and feet; Round as a ball; Always turning around itself.
Glittering points that downward thrust. Sparkling spears that do not rust. What is it?
I am the fountain from which no one can drink. For many I am considered a necessary link. Like gold to all I am sought for, but my continued death brings wealth for all to want more.