I have been replaying through Chrono Cross, and I've just completed the Dead Sea. I think I have figured out my Dead Sea questions, so nobody has to worry about that.
I am, however, still confused about whether or not FATE really cared about Home World.
Not to mention, I'm still not sure what the exact reason is for Serge negating Crono's actions, but I noticed something interesting that the ghost figure of Crono stated:
Crono: The vengeance of the future we killed is about to begin... With Serge serving as the trigger...
Is this what the script means by Serge being the Chrono Trigger? He is the Chrono Trigger that revived the Lavos Timeline? I don't think that the ghost of Crono used the word "trigger" lightly.
Also, could this be a reference to Serge being the Arbiter of the Frozen Flame, which would contribute to him being a Chrono Trigger? I recall that someone in Viper Manor stated that the Frozen Flame was said to have the ability to change history. If the Frozen Flame could do this, and if Serge is the Arbiter of the Flame, then could this be the reason that he is a Chrono Trigger? A Chrono Trigger that will trigger the revenge of the Lavos Timeline?