I would think even more along the lines of the Rings in Rhuidean (though I think those are indeed using the Mirror Worlds, ie: they don't use the "real" pattern to show the future, they show the Pattern branching out into Mirror Worlds because of important choices).

They can show many (an understatement - they overwhelm you with them) branchings/mirrors depending how things stands when you enter them, and what choices you will make. Moiraine has seen many predictions of the future - choices she then rejected because of their outcome. Jordan said the Wheel was like a computer and not sentient, so I think it's also how it works, how it makes its decisions to weave the Pattern. If it needs to pull at a ta'veren, it runs "simulations" by creating mirrors. That's how it determines what factors must be involved for Rand to make this or that choice. Its power is virtually endless, so it can run calculations over many generations. The further in time, the less accurate no doubt, but accurate enough to figure out the great lines very long in advance. The rest of the details, the Wheel calculates much closer to the events, when all the souls involved are present in the Pattern. So millenia ago it decided a woman not tied to any man would give birth to Rand on DM. That was fixed in stone and became a foretelling. The details about Tigraine were projected much later.

I think the Rings tap into these functions of the Wheel, so to speak. Of course the human brain isn't the Wheel, so that's way, way too much projections for the brain to compute. You end up remembering only your key choices.

I'm pretty convinced the two ter'angreal were either designed or programmed by the same women. They have complementary purposes, IMO.

Of course I'm one of those who believe Aviendha's vision was no "accident", that it was the purpose of the Rhuidean AS that one day on the eve of TG a Wise One would be shown the future awaiting the Aiel if they remained warriors and fought. So it's now up to her to make the right choices so it doesn't happen. Like the programming showing the past, it would be linked to the user's bloodline/DNA or something like DNA but linked to souls or however the ter'angreal works, so Aviendha saw her descendants. And this was the final purpose of the Glass Columns. Somehow (her blood, her soul, her bond to Rand... the data collected from when she went in the Rings and was shown it was her who was the Aiel who would marry Rand etc. - there's many possibilities how the machine could identify her as the right woman), the ter'angreal chose Aviendha.

Given all the high tech devices in Rhuidean, it's far from impossible the woman who "guided" Aviendha wasn't a real woman at all but something coming for a virtual reality device set up by the Rhuidean Aes Sedai. She was no more "real" (but no less) than the people seen in the Glass Columns. My guess is that she was from Aviendha's bloodline - perhaps da'shain or more likely Jenn (families split - several bloodlines among the Aiel could very well have Jenn/Tinker ancestors whose offspring joined the warriors at some point) .

I get the feeling we will fully understand those scenes only when the Encyclopedia comes out and we get some of RJ's explanations of how the various ter'angreal really work (if we get that, but apparently that stuff is in RJ's notes and it's where Harriet will go pick her information, so there's good chances we get some stuff like this... hopefully).

I also get the feeling RJ gave us a final mystery à la Asmodean on purpose with this, in the sense that what we saw could very well be the only exposition we ever get about Aviendha's four children, the rest will be obscure clues related to their conception or something like that.

But I would definitely not call Aviendha's vision "prophecy".

It's too bad Sanderson chose to place it not toward the end of TGS but in the middle of TOM, out of chronological order. This appears to change a lot the dramatic purpose those scenes were supposed to have, at least it doesn't seem possible that Aviendha reached Rhuidean after Rand's epiphany, but the way Brandon didn't respect Jordan's convention to order the scenes chronologically in his books, we'll never know for sure. If Aviendha's vision occured after the epiphany, it could be a lot more dire, but that is most unlikely. If she did what she discussed with Amys, she reached Rhuidean between Rand's meeting with Tuon or at most shortly before the WT got attacked. The possible futures were very bleak then, all waiting for Rand.