Regarding the Dead Sea, time at least does seem to flow differently. First, most stuff (but not all) seems to be Frozen in Time, which meshes well with Miguel's statement:
I'm Miguel.
A friend of your father.
According to the time outside,
it's been about 14 years since
the night of the storm...
Curiously, this seems to imply that there are two different "flows" of time existing side by side in the Dead Sea. The static "flow" in which everything is frozen, and a more normal flow in which Miguel, the monsters, and Serge & Squad are able to move around.
Likewise, Chronopolis/The Sea of Eden seems to experience "strange time" as well. That is, it looks like there are temporal echoes between the past and the present (and maybe the future). One might even say that the past/future is bleeding through into the present there. In which case, again we have two different timelines seeming to overlap.
This does make sense given the Time Crash... actually, it may be that the Time Crash is what is responsible for the dimensional split:
In the year 2400, during a
counter-time experiment, the
Flame goes out of control...
This causes the dimensions
to rip apart, resultin' in
the Time Crash.
Engulfed in an enormous
dimensional vortex,
Chronopolis was hurled ten
thousand years back in time.
Because I'm a geek, I can't help but think of the last Star Trek TNG episode in which a rip in time started in the future causes humans not to develop in the past. This would seem to mesh well with what has been said so far; as soon as FATE was sent to the past, it has been monitoring the two dimensions the Time Crash created. Still, there seems to have been an additional influence on the dimensions in 1010, when Serge lived/died, as that is when the flow of time was split. Or perhaps "diverged" might be a better term; two flows of time until then progressing in lockstep. But with the death of Serge, the dimensions began to diverge and FATE lost control over Home World.
However, that isn't a perfect supposition. The 6 dragon gods existed in both dimensions for a time, but in each 3 were removed somehow. The removal seems to have taken place in 1010 as well (that is when the various environments began to diverge from each other, Water and Earth Dragon Isles illustrate). So if the dimensions had existed since 12,000BC (or since 2400 AD, depending on how you want to look at it), why were the duplicate dragons only eliminated in 1010? And why in both worlds?
Setting that aside and picking up the two different flows of time in the Sea of Eden/The Dead Sea, we have a curious statement from the Chief in Chronopolis:
If this experiment succeeds,
we will be able to control time.
We will have complete control over
history and, in a sense, become
a presence, much like god...
This seems to indicate that the time for the city would flow fundamentally differently than the rest of the world; indeed, it even looks like the Chief might be supposing that IF the counter-time experiment was successful, the city would become a presence in time. Which is to say, it might have existed in all time periods (or at least had access to all time periods). If we then place that oddity back into the timeline, we might have two flows of time side by side; Chronopolis' "presence" flow and the area's "narual" flow. That would explain why both the Dead Sea and the Sea of Eden seem to behave as if some things are almost frozen in time while other things are moving apace normal time.
The Dead Sea would have appeared in Home World because the "presence" time of Chronopolis would have remained even when the city was undone. The past, present, and future all sort of being mashed together in that one location.
Course, that still doesn't even approach why the dead sea was formed in the first place.