Answer:
What is it something that you always have but you always leave behind?
When I live I cry, If you don't kill me I'll die.
As round as an apple. As deep as a cup. All the king's horses can't pull it up.
My first is a creature whose breeding is unclear. My second, a price you must pay. My whole can be found in the river of Time and refers to events of today.
I am whole but incomplete. I have no eyes, yet I see. You can see, and see right through me. My largest part is one fourth of what I once was.
I'm the source of all emotion but I'm caged in a white prison.