Answer:
You write on me and secrets I can keep. In places never seen. I spin like a top. Though stiff as a board I'm often described like a mop.
Man walks over, man walks under, in times of war he burns asunder. What is it?
While you were folding a letter you got me. Usually you will do whatever it takes to avoid me but now you can't help but find me.
I am the same written forward backward and upside down.
I always have to work with something in my eye.
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.