How exactly is Noel AT ALL HAPPY in his dream world? It seems more like torture to me. I mean, he's reliving his whole origin story again, with Caius leaving him and Yeul dying, and Noel deciding to constantly wander the world hoping to find a way to Valhalla. At least with Serah, she really did have what she wanted in it, but Noel was just tortured by having to live through that all over again. Caius said he was happy there, and even when Serah watches what Noel goes through in that world, SHE ALSO THINKS HE IS HAPPY THERE! What kind of crap is that? And considering how Caius was Noel's mentor, to have him put through that, its almost like Caius wanted him to suffer.......
He does. Caius' goal is to cause a Time Crash, and the easiest way to do that is for Noel to kill him. The easiest way to do that? Cause Noel so much suffering and pain that he loses control/decides This Is Unforgivable and that Caius has crossed the Moral Event Horizon and kills him. So, if Noel gets out of his mental prison, he'll be more likely to kill Caius, but if he doesn't... well no skin off of Caius' back, he'll just go with Plan B and kill Etro, or even Plan C where he forces open the gate via the deaths of millions.
So what is the exact nature of the relationship between Caius and Yeul?
It's familial more than anything. Caius is the closest thing Yeul has to a consistent parental figure throughout all of her reincarnations, and Caius cares for Yeul as her sworn guardian.
Where were the Farseers between the War of Transgression and the Fall? Were they on Pulse in an area you just couldn't go in FFXIII? Or did they immigrate to Cocoon and then move (back) to Pulse with the rest of the Cocoonians during the Fall? Any evidence either way?
The former. The background material says they survived when the other Pulsian tribes didn't. That's where the Yeul and Caius of AF 10 come from.
How exactly does changing something in the future change the past?
There are three explainations
Quantum Causality that is briefly explained because of Yeul. When something changes in the future, a Yeul in the past has a different vision. If many changes happen, Yeul dies earlier than she originally had. Also, if the Oracle Drive prophecies change, such as they did when Serah yelled at Hope while fighting Adam, then the people viewing them see a different vision and come to different conclusions. In a nutshell it requires affecting people and things in the past which could SEE the future, thus changing their reactions to it in the past.
Reverse Casuality as explained in one of the versions of Yaschas Massif: when you change the future via Paradoxes, the past that leads TO that future has to change accordingly to match up to the "new" future you've created. Essentially, it's reversing causality; the effect needs a cause that could lead to that effect.
Paradoxes: In some cases, things were falling into the past from the future, and Noel and Serah stopped it, thus changing the past.
There are two incidences in-game where the past is altered by your actions in the future. In the first instance, a single paradox effect is linking 10 AF Yaschas Massif with 200 AF Oerba, such that resolving the paradox in 200 AF also removes it from 10 AF. In the second instance, the existence of the seer (100% accurate prediction of the future) means that the past is altered because people in the past witnessed a different future.
During the part of the game where Atlas attacks, Alyssa describes the past being an unopened box with people from the future being observers. Now, you need to be somewhat familiar with the concept of "Schrodinger's cat", in which that our observation "solidifies" the outcome and until then, all possiblilities are happening. In FFXIII-2, a possible future is that Humanity is wiped out. This messes up the past as there is no one to observe history. Thus, by changing the future, you can alter perceptions of the past and ultimately change it.
How could the giant flan disintegrate the crystal pillar from the Sunleth Waterscape? The Waterscape is inside Cocoon, it's not like the flan is disintegrating the pillar from the surface of Gran Pulse...
The crystal pillar holding up coccoon is connected both to the ground of Gran Pulse and anchored to Coccoon itself. If the Royal Ripeness destroys the point where the pillar is connected to Coccoon, then it will fall just the same. Note that in the images of the prophecy of Coccoon-fall, the pillar itself doesn't collapse, Coccoon simply falls from atop it and crushes the pillar on the way down.
All of this was just an excuse for Square to make another sequel. Whether that's good or bad depends on if you like the XIII saga or not.
In the ending, Noel kills Caius, and by extension the goddess Etro, which is what kicks off the Downer Ending. Now, for anyone who saw the secret ending, Caius is still alive, implied that there are several alternate incarnations along the timeline. This raises several questions. First, if the timeline collapsed due to Caius' death, wouldn't all of the alternate versions die with him, along with the alternate timelines? Second, if Caius came back, wouldn't Serah be able to as well, since the laws of life and death no longer apply? (Keeping in mind that Caius died before Serah.) And third, if Caius IS back, wouldn't Etro also be back, since his living is directly linked with the goddess, since they share the same heart (in a way)? Also, if there are several Caiuses, then there would be several Etro hearts, which would mean several Etro's, meaning she could never really die unless ALL the versons of Caius died. Maybe. Just throwing it out there.
It's pretty clear from what Caius says that Caius is somehow alive without Etro.
In response to your first question: Caius survives because he exists in Valhalla, a world outside of linear time. If Time is a linear book, then Valhalla and Caius exist outside of the pages. In Valhalla, all events effectively occur at T=0s. Caius enters Valhalla at T=0s, Caius fights Lightning at T=0s and Caius is killed at T=0s. So thanks to Valhalla's non-linear time, Caius effectively exists and dies at the same point in time (T=0s), and it is the former of those two Caius's that continues his plot even after the latter is killed. Incidentally, this non-linear time is also the reason Lightning is able to appear to Serah even after she has been defeated by Caius in Valhalla.
According to the official mythology, Valhalla isn't just another dimension outside time — it's the afterlife of the Final Fantasy XIII universe. Caius is dead, but that doesn't matter anymore. The time collapse has basically made the living world the same as Valhalla, so that there is no longer any difference between life and death. That should mean the same should go for Serah, but hey, Rule of Drama.
However, why Serah wasn't brought back aswell could easily be explained. Since she could see the future like Yeul, that could mean like Yeul, Serah could've been reincarnated aswell, thus she wouldn't be the same as her previous self and would be a completely different person. Meaning, she could be someone we meet in Lightning Returns.....
Where DID Snow get his new l'Cie brand from? It's a Pulse brand but what fal'Cie cared enough to brand him? What timeline did that happen in? Just bothers me that they never touched on it after he went poof.
It's in Final Fantasy XIII-2 Fragments After, a book available only in Japanese.
How come when Caius died by Noel's sword, Noel didn't obtain the Heart of Chaos?. Was it because he didn't actively kill him since Caius stabbed himself and hence didn't obtain the right to wield it? There is the Paradox Ending Heir of Chaos but still ...
Because he didn't claim the Heart. Similarly, considering how Valhalla is a land where life and death have no meaning, how can Caius die at all?
Did they ever explain how or why Serah and Noel teleported while fighting Atlas? It wasn't addressed and is never mentioned again as far as I can remember.
So why did Serah change clothes in the beginning of the game? Schoolgirl clothes wouldn't really fit in a journey, but was it just a paradox?
It's mentioned later on in the game that she carries a mark of Valhalla, which by process of elimination must be the clothes she gets; the engraving in the middle definitely seems Valhallan. It's similar to Lightning's change of outfit - new clothes, new powers, new responsibilities. They probably also represent her being gifted the Eyes of Etro.
The only way for the Heart of Chaos to stop beating is when someone stabs him in that heart and is of strong will to reject it. If not, the heart would just go into the person who killed him. It's possible that Caius knew his will was too weak to reject the Heart of Chaos should he commit suicide, and that's why he trained Noel to do so.
In the secret ending of the Lightning DLC, Lightning goes into crystal stasis for eternity and... wakes up in a distant future after eternity. How can there be such a thing as "after eternity"? How can there be such a thing as a distant future at all when time doesn't exist anymore?
That's exactly the point: nothing should exist anymore after Chaos consumed it. The fact that there is still anything left after that... that heavily implies Etro isn't completely dead, somehow, possibly because of the crystallized Lightning. It makes little sense, I admit, but the story is clearly gonna continue, most likely explaining things there.
Hope's plan to save the future. Building an entire new floating world is stupid. For one, in the time it took to build this thing (approx 500 years from when they learned Cocoon would fall), they could have simply moved all human settlements far away from Cocoon's base, so the impact would have little damage. Heck, they could have just disassembled the old Cocoon so there'd be nothing left to collapse. What's worse, is repeating the whole "floating world" thing just makes it easier for a repeat of XIII's events to occur, by Caius or anyone else that wanted to destroy everything, by giving them one single target instead of spreading humanity everywhere across Pulse. I understand that Hope wanted to save Vanille and Fang, but I'm starting to think that Bhunivelze is only there as a shorthand for showing the entire human population destroyed by chaos in the ending, and to Mythology Gag link the ending to a soon-to-come XIII-3. There are just too many negatives and too few positives to a plan like that when other options are way more feasible. Sure, Caius would find a way to stick his nose in everything, but why make things easy for him?
Look at A Dying World (700AF) and New Bodham (700AF). That is what has become of Pulse's landscape and ecosystem two hundred years after Cocoon falls. That is why simply spreading out the human settlements to minimise casualties would not have been a long-term solution. See Colony Drop for more possible consequences of a moon-sized object crashing into the Earth. As for disassembling it, Hope didn't order Fang and Vanille's crystals removed until the structure was about to fall anyways. From this we can infer that they didn't want to risk it falling early. This is a moon sized object, not a skycraper, so the risks are much greater if something goes wrong. This leads to the possibility of Caius sabotaging the disassembly as he does the the launch of the new one.
If Caius' plan was to end time by killing Etro('s heart), why didn't he just commit suicide to begin with? Why go through all this stuff? Why not just go into Valhalla and kill himself?
In the Valhalla prologue of XIII-2, we see a big round thing in the sky as Noel falls from the sky. Fast-forward to the end of XIII-2 and we see the world turning into Valhalla with the New Cocoon/Bhunivelze in the sky. Could it be that the entire story of XIII-2 is one giant Stable Time Loop? That, even during the prologue, the end was already set in stone and the part of the ending where Lightning is crystalized on Etro's Throne actually takes place just a few minutes after the prologue?
There is alot of speculation around that theory, but as far as possibility is concerned... it does work. As mentioned above, for Valhalla everything in it is happening at the same time, its explicitly a Place Beyond Time, meaning that everything is effectively simultaneous, while also being infinitely far apart. Lightning's prologue battle with Caius, as well as every other implied battle between the two, happened seconds, minutes, hours, days, weeks, years, decades, centuries, millenia, etc., before the finale all at once, and none of them at all. It's entirely possible that the very existence of the prologue makes the whole game a Foregone Conclusion: the very fact of Valhalla existing means that time has to end and the protagonists will fail.