Well, the wormholes aren't just open passages anyone can use at their leisure. FATE can, or more like, can open up for others to use them. As for how Serge did, well, it's thanks to the dragons. When you approach the distortions after the HW Fort Dragonia events, a message appears about Serge being now worthy and to go challenge fate. So it's not that Serge had Lynx's body (which, when you consider things, he never really gets his body back, just his DNA to reshape it back to his own's image), it was that FATE would not open them up for obvious reasons, while the dragons decided he needed his DNA back first before they open them up (which makes sense, when you consider the room to the Frozen Flame is behind a DNA-sensitive lock, that even FATE can't open up).
No, Lynx can enter Chronopolis itself just fine. It's only the room with the Frozen Flame that is out of bounds, again, because of the DNA lock. Which is the reason behind the whole body swap incident.
Well, the entryway had to be sealed off between 1017 AD and 1020 AD. If the Fiddler Crab can open it up there is no reason it can't be the thing to seal it off as well, considering the whole tide thing, which means anyone with the object can do it. Pearly Gate opening up could be an oversight. Since at that point is when they decide to head into the Sea of Eden, and now all of a sudden the place is open to trigger the "get the six dragon relics" part of the plot. But well, how to know the exact intent? About being more than one... well, logic dictates there has to be at least two, one per world. So yeah.
No, I would think FATE already knew, specially by 1017 AD.