The oppertunity cost is ~$0. It can be merged mined right along side Bitcoin. The hardware, labor and electricity would still be spent if one was only mining Bitcoin. Nobody is mining this at a loss it is just a free bonus on top of the BTC.
To be fair, while it is low, it is not zero. Running it takes up cpu and memory and network resources etc.
But aren't those cycles already 100% used for bitcoin? That's how I understand it. You get the other merge mined coins literally for free. Frankly I don't see how the same cycles can hunt and decode different mathematical puzzles without taking away from the main task, but that's what I've heard from a lot of pros on here.
No, only the mining hashing cycles are common. You have other cpu cycles used by the daemon still being used. Now if you are just mining, and using a pool, those costs are born by the pool, so you will not see them directly as a pool user.