1. It's complicated. It's important to keep in mind: Sora did NOT travel back in time to save his friends at the Keyblade Graveyard. It only SEEMED like he did. After Sora and the others got killed by the Demon Tide, Sora appeared in the Final World, where Chirithy helped him piece himself back together into his physical form that Kairi was holding together via her Princess of Heart powers. After piecing himself back together, Sora returns to the Realm of Light by using the power of waking. Now, normally, the power of waking is supposed to be used in tandem with people's hearts to either return them to their original state, or to travel to worlds that they've personally been to. But in this case, Sora uses the pow to travel to worlds by using the hearts of the worlds themselves (this is what happens when Sora is diving into the different world portals to chase after the Lich), which as Young Xehanort states, is a big no-no. Once at each world, Sora encounters his friends' hearts and souls which are in the process of being dragged off into the darkness by the Lich. Sora uses the power of waking to resurrect them back to life. But this is another gross misuse of that ability: the power of waking is supposed to be used to return a heart to its original state, which is technically what Sora is doing (returning a dead heart back to its original living state), but of course, this is not how the power is intended to be used, and it runs counter to the laws of nature. Because of how many times Sora flouts this cosmic law, he disrupts the universe to such a degree that it creates, as Nomura put it, "a singularity" that completely screws up the timeline. So, when Sora returns to the Keyblade Graveyard, again by using the power of waking to travel there directly, the universe tries to course-correct by resetting everything the way it was before the incident. This is why the sequence that plays out between the Guardians and Terra-Xehanort is exactly the same—in that moment, the universe basically tried to "forget" what had happened, and made things so that the same event would play out again as they were supposed to, causing everyone to get momentary amnesia and just go through the motions again. However, Namine, whom Sora had spoken with in the Final World, was immune to this, because she was able to reach out to the Lingering Will directly from the FW, which is itself outside of space and time. So, the universe wasn't able to erase her memory like it was with everyone else, allowing her to influence the new course of events. So, essentially, what happens the second time through is actually the exact same timeline as what happened the first time—in fact, it happens directly AFTER the first run-through. The universe just "forgot" it had happened before and basically pretended like everything was happening again for the first time, effectively starting everyone and everything back over from square one. But it was NOT time travel, and Sora did NOT create a new timeline by doing this. Sora was NEVER able to actually rewrite history, which is why he wasn't able to change the outcome of events when he went back the second time. The first time was less time travel and just a massive cosmic disruption that resulted in a do-over.
2. Future Sora restored both Xion's and Roxas' hearts. He unlocked both of their hearts from his Station of Awakening after both their hearts became awoken by the conflict going on between Sora and Xehanort-controlled Xion on the outside. After unlocking their hearts, Xion's heart transferred to her body, causing her to regain her memories (this happens at the moment when she starts crying and clutching her head), and Roxas' heart leaps out of Sora into his incoming replica vessel.
3. Well, Xion was created as a vessel to extract and contain Sora's power and memories. To do this, in 358/2 Days, she unknowingly sapped those memories and powers through Roxas, who was Sora's Nobody, and thus acted as a conduit for those things. Namine approached Xion and they both agreed that in order for Sora to be recompleted, he would need to be rejoined with Roxas, but Xion was making that impossible because of how she herself was absorbing Sora's powers and memories out of Roxas. The only way to undo that damage and make sure that Sora could be awoken whole and intact was if Xion gave all of those memories and powers back to Sora. A natural consequence of this, however, was that everyone who remembered Xion would forget that she existed, since all the memories that belonged to her would return to Sora, effectively becoming HIS memories, thereby making it as if Xion herself never existed. This is also a result of Namine's unique abilities to manipulate the memories of those connected with Sora. Once Xion's heart returned to her body, we can assume this effect was negated, and now that she was her own person again, she and everyone who knew her regained their memories of her. We can see this happening with Lea the moment Xion's hood is uncovered.
4. After being possessed by Master Xehanort in BBS, Terra's heart shared space with Xehanort's inside his body. During the final battle against Aqua, Xehanort also created the Guardian to act as both a defensive/offensive weapon but also as a container in which to transplant Terra's heart and mind, which were causing him consistent trouble in maintaining control. After losing his memories, Terra and Xehanort's hearts both shared space within the entity known as Apprentice Xehanort, but because both Xehanort's and Terra's minds were afflicted with amnesia, there was less conflict within him, as neither mind could remember who they really were or what had happened to them. After becoming Ansem Seeker of Darkness, Terra's heart went with Xehanort's and resided in the same Guardian creature that Terra-Xehanort had created, acting once again as a weapon and container for Terra's heart. After Ansem's defeat, and after Xemnas' destruction, both Master Xehanort and Terra became recompleted into their original selves. But since Master Xehanort still needed Terra as a vessel for the coming Keyblade War, he re-possessed him with his own heart which he had his younger self (Young Xehanort) bring forward from the past (in other words, MX planted the heart of his BBS self into Terra's recompleted body). Now, this new Terra-Xehanort was again able to use the same old trick of using the Guardian as a container for Terra's heart so he wouldn't interfere. Once Terra-Xehanort killed the Lingering Will, which was Terra's mind taking residence in his Keyblade armor, his mind rejoined with his heart inside the Guardian, giving Terra the semblance of identity required to successfully fight back against Xehanort's control once he was defeated by Sora, Aqua, and Ventus at the Skein of Severance.
5. Because Mickey has telepathic powers. He was also the one speaking to Sora in those dream sequences in KH1, as confirmed by the KH1 Ultimania. So, he can just do that.
6. Who knows? It was just a weak excuse to have the Data battles that all the fans were demanding. If I had to guess an in-world explanation, maybe they thought that one of the Organization members might have had some idea of where Sora's heart could have gone, and that their data recreations might hold that same information because data in the Kingdom Hearts universe is basically just science-magic.
7. Unknown. My only guess is that Sora wasn't ACTUALLY there, but was merely able to manifest there because he was residing inside Terra's heart at the time, and since the battle between the LW and Terra-Xehanort was basically a battle between Terra's mind and his heart (which was inside the Guardian), maybe Sora was able to pop out into the physical world for a brief while as a result of that friction. The truth is, though, I'm just not sure.
8. Namine was able to located Terra's mind from the Final World due to Sora's previous encounter with the Lingering Will in KH2, and since Namine's special powers relate to everyone connected with Sora, she was able to track Terra's mind and influence him from the Final World.
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