Answer:
I have one eye. See near and far. I hold the moments you treasure and the things that make you weep.
What has a bell but isn't a church. Is full of air but is not a balloon?
I am two-faced but bear only one. I have no legs but travel widely. Men spill much blood over me. Kings leave their imprint on me. I have greatest power when given away, yet lust for me keeps me locked away.
My first is in blood and also in battle. My second is in acorn, oak, and apple. My third and fourth are both the same. In the center of sorrow and twice in refrain. My fifth starts eternity ending here. My last is the first of last, Oh Dear.
Three little letters. A paradox to some. The worse that it is, the better it becomes.
People take me on walks and I run and have fun. What am I?