Answer:
I'm a type of pizza that is folded in half before cooking to contain a filling
The eight of us move forth and back. To protect our king from the foes attack.
I grow for a surface, even if you cut me. I continue to grow even after death.
I can run but not walk. Wherever I go, thought follows close behind.
Runs smoother than any rhyme, loves to fall but cannot climb.
The warmer I am the fresher I am.