Answer:
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.
What is the smallest bridge in the world?
Take off my skin, I won't cry, but you will.
What can run but canβt walk?
What is full of holes, but can still hold a lot of water?
Iβm grown from darkness but shine with a pale light. Very round I am and always a lady's delight.