Answer:
I am the kind of nut that is empty at the center and has no shell.
My head and tail both equal are my middle slender as a bee. Whether I stand on head or heel Is quite the same to you or me. But if my head should be cut off the matter's true though passing strange directly I to nothing change.
With a halo of water and a tongue of wood, stone as skin long I stood. What am I?
I have a brother. However much we run we do not reach each other.
I roam through the lands hoping to rescue my love. I search high and low and will stomp on you if you get in my way!
I am owned by Old McDonald.