Answer:
I can wave my hands at you but I never say goodbye. You are always cool when with me even more so when I am high!
I have two bodies joined together as one. When standing still, I run and run. What am I?
I am a portal to another world which you cannot enter. Only you can see me but I can't see you.
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 have a head, tail, but no arms and legs. What am I?
Though not a plant, has leaves. Though not a beast, has spine. Though many wouldn't need this thing, It's more valuable than wine.