Answer:
I go through a door but never go in and never come out.
If you have me you want to share me. If you share me you don't have me. What am I?
I have all the knowledge you have. But I am so small that I can fit into your hands. What am I?
Tear one off and scratch my head what was red is black instead. What is it?
The higher I climb, the hotter I engage. I cannot escape my crystal cage. What am I?
It flows out of the soil, It burns you if it boils, And holds us in its coils, More valuable than gold, As black as it is old.