Why did the world split in two (BTW, Sentenal, I think of the split exactly as you do)? Was it because Schala sent Kid?
It split into two because of Serge. Wazuki drowned him, but Kid traveled back in time and saved him. Serge has full memories of dying AND living at that time. A paradox that caused a time split. My theory is that as an Arbiter, Serge can remember changes in timelines even if he doesn't have TTI, causing time splits if he has two sets of memories plus his powers as the Arbiter giving him uberly awesome time powerz.
Why did Schala send Kid? In other words, what did Kid do that the people of 1010 A.D. couldn't?
Apparently she sent Kid so that there'd be someone out there to help free her. She planned out Kid's existence so she could save Serge.
Exactly when did Kid come to the world? Before the split? After? Then, how old is she?
She's only a year younger than Serge, so about two years before the split, I think.
When did FATE create El Nido? How does FATE control both worlds?
About 10,000 years ago. FATE controls everything in El Nido with the Records of Fate, little devices that act as routers for FATE's influence. The Records don't work in Home world though, so um...uh...I think FATE has limited powers over time and space, considering what it IS.
Since Lavos is dead the latest in 1000 A.D., why is Schala trapped with the Time Devourer?
Well, when you change the future, it goes to this place called the Darkness Beyond Time. It's a junkyard for old timelines and dimensions. If you kill Lavos, then his future self, how he would live if he wasn't killed, would be sent to this junkyard. Schala was sent there through a vortex created at the Ocean Palace (Like the ones that sent Janus and the Gurus through time) and found herself in the Darkness Beyond Time with Lavos.
What exactly is the Time Devourer? Lavos in some form? An entity of the planet? The Entity? The Planet? Both? What's the purpose of the Time Devourer?
The Time Devourer is Lavos and Schala merging together into one entity, boosting their powers to phenonemal levels. So yes, I guess you could say Lavos+Schala=Time Devourer. The Time Devourer is an anomaly, a mess-up, and oopsie of reality, and when it grows up, it'll eat all of time. It'll eat every second in the entire universe and time will cease to be. It will basically delete the universe, leaving only the Time Devourer, which I guess might starve to death or something.
Why isn't the Sea of Eden in Home World as it is in Another World? Why Chronopolis isn't in Home World, too? Or why isn't the discarded future in Another World, too? Just because Serge is alive?
Serge created a paradox. As the Arbiter, he has control over the Flame, and not FATE. So FATE tries to kill him to get the Frozen Flame back, but this causes the time split, as we all know. When Crono and crew went to the future and stopped Lavos, they could only go to one timeline. Now that there's two 1999's, Crono and crew will only travel to one of them, Another, the real 1999. So the Lavos in Home World will live, and because of this, FATE won't be created in Home 2400, so it can't travel to the past to make El Nido. It's a paradox, so because of that, the Sea of Eden in Home World became the Dead Sea, a mix of all these destroyed timelines from the Darkness Beyond Time.
In which world did FATE or the Frozen Flame turn Wazuki into Lynx? What happened to Wazuki in the other world? What happened to Miguel in Another World?
Wazuki turned into Lynx before the split, so it happened in both. In Another, Lynx does what he does in CC. In Home, he tries to get the Frozen Flame from the Dead Sea, but only the Arbiter can survive in the Dead Sea, so he got frozen and died. Miguel in Another World, I assume, was killed off by FATE.
How can Harle be the seventh dragon? She doesn't look like the other six just a bit. When was she created? Why does she follow Lynx?
She's the seventh dragon because the other six created her. She was created during the period where Chronopolis crashed, temporarily weakening the seal on the Dragons. They used this time to create Harle, a dragon not sealed by the Frozen Flame's power. She follows Lynx so that he'll lead her to the Frozen Flame and then she'll backstab him and set the other Dragons free.
Is the Frozen Flame a part of Lavos? Does it exist in both worlds?
The Frozen Flame is a piece of Lavos that broke off when he landed in 65,000,000 BC, so yes, there's a Frozen Flame in both worlds. However, the Frozen Flame in Home World was in the Dead Sea where no one could reach it, and when the Dead Sea was destroyed, so was Home's Frozen Flame.
What caused the Time Crash? The experiment in Chronopolis? Since Chronopolis was sent back, to which year was it sent?
Lavos caused the Time Crash to pull Chronopolis back in time so it could ultimately save itself. It was sent to 7600 BC
When was Terra Tower created? In which timeline? I thought it was in the Reptite Timeline, but then I saw the scene with the attack (in the fake Viper Manor) and couldn't understand how the humans attacked Terra Tower.
The Reptite Timeline. It was created in the Reptite Dimension as a counterpart to Chronopolis, and when the Time Crash happened, Dinopolis was pulled into Chronopolis's time and dimension to counterbalance it.
Is Terra Tower the Dinopolis?
Yes.
What happened to Kid after the party saved Schala?
No one can really say for sure. Some say she still lives with Lucca in a repaired timeline, some say she merged with Schala. I personally believed she was erased from existence when her birth was overwritten by the uniting of the timeline.