As far as I can guess from my limited (a bit of interest) knowledge of Astronomy and Astrophysics, the big "Saturn like Planet" is actually the "planet" and Atys is a moon orbiting it.
So is the other "moon" we see in the sky.
It too is in a geosynchronous orbit around the "Saturn planet", only one slightly higher than Atys.
(Remember, big Planets like Jupite,r or Saturn for that matter, can have more than one Moon.
Some even with their own Atmosphere, if they´re big enough themselves.)
The many falling stars we can see in the nightsky are nothing more than debris from the planets rings entering the atmosphere of Atys.
So Atys revolves around "Saturn II" slightly outside its ring-orbit.
The Ring probably being the devided mass of a former moon, that was torn apart by the big planets and the other moons gravitational pull, some millennia ago.
Atys and its "sister moon" thus being in the very fortunate position of balanced gravitational pulls.
As for the Sun staying in the same place, it all depends on the synchronousness and form of orbit and the spin of Atys itself. If the night as we see it on Atys isn´t caused by the moon itself revolving around its axis, but by it entering the parent planets shadow at a certain angle, it would cause the sun to look like it was fading and reappearing over time. While actually Atys would move away from it and in addition enter its parents shadow, causing darkness and coldness.
Atys could very well be rotating at the same speed as the planet "below", just as earth-moon does, causing us to always see the same site of it. (Bound rotation) just as from the planet below one would always see the same side of Atys.
Phew... all else regarding other "continents" has been said already.
Atys is quite big, and I´d be quite surprised if the New Lands would be all there is to it

CU
Acridiel