is it possible—geographically—for a piece of mass to drift from the northern region?
Is it theoretically possible that on another world a land mass could drift from one hemisphere to another ? Yes. There's just no reason it can't, but such drift is slow and it would take a very long time.
According to their [elves] history, a piece of land floated away from the north
This is not something any society without near immortality is likely to have a record of. The timescale for such a process is hundreds of millions of years. Most species won't last that long (the elves would likely be extinct before you need the map) and the idea of historical records surviving that long is extremely unlikely - I think we have at least one Q&A on that subject.
A myth might develop that such a thing happened. Alternatively Elf scientists might discover that such continental drift occured and have a reasonable hypothesis that appears to show that the original location was in what is now the southern hemisphere.
and then the "water people" sunk it.
I have no idea how your sink even a small continent (or even an island). Any culture capable of this would make darn sure your elves were all dead and make a good job of it. The event itself would make it practically impossible for any records of the prior drift to survive and the survivors would have a heck of a lot more pressing needs that maintaining historical records (for generations to come).
When we look at the world map, you can see the north is smooth than the south. You get all the mess as you go down, but north is comparatively smooth.
Go tell that to the Alps, Urals, Rockies and the Himilayas. I have no idea why you think this difference exists. There's certainly no basis for such a difference in a general sense that all planets would need to have it.