Major spoilers ahead. Proceed at own risk.|
The main plot of the story involves something that happened in Chrono Trigger. Crono and his friends managed to defeat Lavos in the end, and as a result prevented the Day of Lavos. However, if you remember correctly, Crono and his friends knew about the occurence of the Day of Lavos in the apocalytic future, Robo's time. Hence, Crono and friends could not have stopped Lavos if they had not seen the event unfold in the apocalytic future. In other words, the apocalytic future must exist in order for Crono and friends to stop Lavos. This causes a split in reality, and results in a dual-dimension. One is the one where Crono stops Lavos and results in a good future, and the other is where the Day of Lavos occurs and results in the apocalyptic future.
Fate, a supercomputer from the future, tries to repair this dual-dimension problem, but only succeeds in causing parts of the apocalyptic future to leak into the other dimension. Some of the effects of this is that building you saw in the vortex, the futuristic one, and also that structure that was formerly known as Crescent Island. To rectify his mistake, Fate sends Yamaneko to rectify it, and to do this Yamaneko needs the Frozen Flame.
The relationship between Yamaneko and Serge is one that I'm a little confused about. It is known that Serge was called to the Another dimension by Fate, the part where Serge had some kind of a flashback. Actually, Serge is a victim of a very heinous loop. The Serge that you start with, is actually the Serge that is from the Another dimension, and will die later (the tombstone). The real Serge, the one from Home, is the one that becomes a baby at the Dragon Temple. This actually explains why Serge had flashbacks of being a panther early on, since he became Yamaneko for a while. Confused already? To add to that, ultimately, the Serge used in the end comes from Yamaneko, right? And wasn't Yamaneko's purpose to rectify Fate's problem? Didn't Serge do exactly that in the end? Am I getting more and more confused?
The most important element in Chrono Cross is Sarah, better known as Schala to the ones who played with Ted Woosley's translation. In Chrono Trigger, Schala's wherabouts were unknown after she was thrown into the time vortex with Lavos. It seems that she has been stuck there all the time with Lavos, which explains that little girl in Lavos when you fight it in the end. If you have seen the ending of the Playstation version of Chrono Trigger, notice that in the end, Lucca finds a baby with Marle's pendant, which is actually Sarah's pendant as well (Marle is Sarah's descendant). That baby is Sarah, or better known as Kid. What about the Sarah with Lavos then? Well, notice that everyone has an alter ego in each dimension? Well, Kid's alter ego is stuck with Lavos. The whole Sarah stuck in Lavos is the cause of the whole problem in Chrono Cross. That's why Project Kid was done, in order to extract Sarah from Lavos and restore things back to normal in the process. In the end, Serge had a simple choice to make to restore things back: destroy Lavos along with Sarah, or save Sarah using Chrono Cross.
Most of this information was related to me by someone who knows Japanese. If I'm wrong anywhere or you would like to add some information to this, please contact me.