It doesn't seem at all plausible to me that a damane could be a darkfriend. They are completely subjugated. People become darkfriends for personal gain, but how would a damane expect to gain something? Unless Alivia is the one damane in all of Seanchan that was able to keep a sense of self even after 400 years of being a tool to be used by other people. Sounds unlikely.

The notion of her being a Seanchan spy seems more likely.

I'd say you're right that the Wheel was showing off, but that it had a good reason to do so. The Wheel spins out the Dragon, right? Well, part of what "the Dragon" is all about is the mystique that surrounds him and the effect it has on people. A person doesn't attain the status of hero just by fighting and defeating evil, they have that something special that sets them apart. So part of the Wheel's spinning of the Dragon is making that mystique, especially when Rand isn't making it himself yet.

Also, I don't think it makes sense to debate whether it was "the Wheel" vs. "the Horn". The Wheel spins all things out, right? So it all comes back to the Wheel.