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 comes once in a minute, twice in a moment, but never in a thousand years?
I pass before the sun, but make no shadow.
What kind of table has no legs?
I am always hungry, I must always be fed. The finger I lick will soon turn red.
I am the fountain from which no one can drink. For many I am considered a necessary link. Like gold to all I am sought for, but my continued death brings wealth for all to want more.