I never thought that the Dead Sea was Chronopolis... It's no where to be scene. Remember, Chronopolis never existed in the Lavos Timelie, so it can't be there.
As for the Data Banks, I truely believe that they were not guarding Chronopolis. They obtained all the information, but when Serge got close, they had to flee, that is why we still had to fight that monsters. That Monster was the guardian of Chronopolis.
About Miguel, i'm pretty sure it was hard but was easily done since it could be either Miguel from another or home. Either way, FATE could have binded him using the dimension distortions.
Also, about Miguel, was he and Wazuki held captive at Chronopolis and only Serge escaped? Or what? Otherwise if they escaped, then there would be 2 Miguel's, we all know that Wazuki became Lynx before the dimensional split and then theres 2 Serges, one died. So where is the other Miguel? Could it be Home's Miguel?
And on the topic of Lynx, I'm pretty sure FATE controls him when she wants to. Like Lynx doesn't seem like a computer all the time. I'm pretty sure Wazuki is still in there somewhere. Wazuki goes mad, FATE implants itself into his brain. His brain switches into Serge's body. I don't truely think that Lynx's body and Lynx is truely FATE because I remember the little children, probably Crono saying that FATE wanted to use the FF power to turn itself into a human one day.