Gliese 581-G (Just for fun)

[acrosome]

Yes, a moon would be unlikely. Unless it were a recently captured vagrant.

With a giant ball of fusing gas in a predictable location in the sky, I doubt that the locals would care much about magnetic compasses. It would be pretty damned easy to fix your latitude, just by measuring the height of the sun above the horizon. As always, fixing longitude would be more of a challenge. In fact, my mind boggles on a way to do so, even with accurate clocks. Perhaps with very accurate stellar measurements, but that could only work near the ice zone where you can see the stars. The stars also wouldn't wheel around the pole star (if there is one) as quickly as they do on Earth- instead, one rotation would take one year.

More intersting is how they would define direction. North/South/East/West makes little sense. Perhaps they'd use a polar system instead? Clockwise, Widdershins, Axial, and Radial? (With Axial defined as "towards the spot where the sun is directly over head," and Radial as the opposite.)

Also, there's really no reason to expect the hot side to be all land, is there? There'd be no ice given the model you're using, true. But there might be a sea crossing the hotside pole. Land might run right up to the ice sheet in some spots. Etc. Because, yes, the planet would be pulled into a bit of an egg shape, but that tidal force is acting on the water too, so you can model it as a flat surface. High points are high, low points are low (and full of water, which is rapidly evaporating at the hotside pole).