If I have "In the Eye of Chaos" and "Melek: Izzet Paragon" in play and I cast an instant, do I have to pay the x cost for Eye of Chaos for the copy of the instant?
You still have to pay (X). I realize this is confusing with In The Eye of Chaos’s printed text, but if you check out its Gatherer page and read its Oracle text:
http://gatherer.wizards.com/Pages/Card/Details.aspx?multiverseid=202410
then you’ll see ITEOC’s ability is now written as a triggered ability.
When you cast an instant spell – regardless of how you paid for said instant – ITEOC will trigger, and that trigger will go on the stack ahead of the spell. When the trigger resolves, you’ll have the opportunity to pay (X). If you don’t, the trigger will counter the spell. This all occurs after you cast the spell but before it resolves.