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 liquid can contain the soul?
I'm full of holes, yet I'm full of water.
What can burn the eyes, sting the mouth, yet be consumed?
I can be written, I can be spoken, I can be exposed, I can be broken.
What is lighter than what it is made of?