This is likely a case where most of the details will be wrong, though I think it brings all the prophecies/foreshadowing together:

- "the future/the world" can hardly tethers on the edge of a blade after the LB. Even a general Seanchan vs. Westlands war wouldn't threaten the Pattern enough to account for that. So IMO, this suggests Rand will appear to be dead, his life hanging by a thread, a last spark of life no one but Flinn and Nynaeve linked will be able to fan again, but this will happen as the LB begins, at the end of TOM. This has to do with "the world is one with the Dragon". Rand being "dead yet alive" will plunge the Pattern to the brink of unravelling as well, providing the necessary "darkness" for the LB. This is when the Asha'man and AS will become one, when the three in a boat scene will happen, etc.

"Belief and order makes strength" I've half-covered in the previous post. I think belief refers to the ability in TAR to make real what you believe to be real. There will be an army of wolves, with memories going back very far, who remember the Pattern without the Bore and the Blight. They will be the collective minds using "belief". They need Perrin as their interface with humanity. All they will need then is a Guide to show them what to do and help them, a "super dreamer". This, I think, will be Egwene's task. My idea is that this will have to happen with tel'aran'rhiod is folded with the real world so that what happens in TAR affects the real world (and that will be possible because of "Order" - the dreamwalkers will show what needs be, the Wheel will make it all happen). Which leads me to my second intuitive leap (a big one at that!): Egwene is a Hero of the Horn. With Rand, they form a couple of Heroes like Birgitte and Gaidal - always tied together - yet very different from the two lovers: they have cycles of opposition/union (like saidar and saidin, together and in opposition, like fire and water, like moon and sun), and it's through this dynamic the Wheel uses them to correct the Pattern. So, Egwene will turn out to be Latra Posae reborn, and one of the Heroes.

So, according to my theory, she might be the second woman who links with Rand (the other is Alivia) for the "decoy" to fool Shai'tan, and she will die with Rand, and think that doing so she puts her very soul in the balance. The moment they die, Mat will sound the Horn, bringing both back (it was hoped for about Rand, a surprise about Egwene. Alivia will die the final death, alas). Brought back by the horn and dead-alive, standing both in TAR and the real world at once, Egwene will be the "super-dreamer", the wolves and the dreamwalkers will be her "believers". Once brought back, Rand will kill Moridin, and lead the Heroes into "heroic stuff" (eliminating sources of chaos), channelling for all he's worth now that it's safe - finishing up the Shadow's forces, in coordination with Mat leading the "live" forces. Perrin will have entered TAR to be with the wolves, and he will be Egwene's interface with the wolves.

The other key to victory is what I have tried to explain above, ie: Order. I think 'order' will be the same thing as bringing the whole (the four corners of the) world together "as one". WC and AS, AS and Seanchan, all the remaining rulers and armies, all the channellers as one unified group, beasts and humans, all the sentient races (Ogier, Finns etc) together as one, the Da'shain reunited too and singing (this should contrinute to helping the area of SG "heal" fast enough, and as I said I think the Finns will also do something through their connections with Mat). All of these held together at SG by their links to Mat, Perrin and Rand.

Rand's blood poured on the rocks bringing salvation will be the two wound opened together with Justice (the wounds slashed opened by Alivia, IMO, after SH brings Rand to the brink of death maybe, unable to sheathe the blade in his body himself), the two evils mixing on the rocks, causing the Pit to explode.

Twice dawns the day will refer to the fact that when Rand dies, the world will appear to die too. The night will fall, absolute darkness will fall and reality will ripple as it never did before, until Rand returns with the Horn ("the dead shall be ward against the fall of the long night", and with that the Shadow will dissipate, and the sun will appear to rise again. And as the Neo-Da'shain sings, Rand will be He Who Comes with the Dawn for real.

I think the "big surprise" RJ has in store is that Egwene too will die in the Pit alonside Rand, after she's brought the channellers together as one. This time Rand and her now work together. In the AOL, there were needed to work against one another. LTT's plan was flawed and could not happen as he devised it (it would have tainted both halves, dooming the world). Latra Posae's Concord took care of that. Her plan was flawed too, but it was vital as well: she made the CK, which were nedeed to cleanse saidin (and other things, like making Rand understand the real danger of that much OP, and also to provide him with enough power to resist a TP addiction - the alternative path he could take after touching it a first time. But he had an even more addicting quantity of saidin to play with, until the moment he had his epiphany and can resist the TP all on his own now). Latra Posae also completed LTT's War against the Shadow after the Sealing.

Now Egwene and Rand have worked against one another, Egwene keeping the WT out of Rand's hair, and bringing about the alliance of all channellers for the LB. At the end, they will be side by side this time, and die together. I think Egwene as a Hero is also some kind of "Guardian" of tel'aran'rhiod. She is its real "mistress", after a fashion. After she dies and return to TAR, she will be the protectress of Dreamers and the denizens of TAR, like the dead wolves and Heroes.