Christanos (and presumably those dark elves that she deemed worth keeping alive) retreated deeper underground after the Foreign Quarter was destroyed. It's entirely possible that they moved the city with them, abandoning the old quarters that remained standing. This would make sense in light of the Rending, which could have caused the rest of Old Neriak to cave in.
As for why the entrance to Fallen Gate is located in the Commonlands, keep in mind that the entrance we use now isn't the original entrance to Neriak. We had to find a new way in, and the new entrance just happens to be accessed from the Commonlands.