I can think areas where running is a greater advantage, and areas where swimming is a greater advantage, and different musculatures may account for each... but in pretty much all areas generic intelligence is an advantage.

This doesn't preclude the possibility for differences, but it's a reason why the differences wouldn't be as strong.

No, I don't think we can really say that unfortunately.

I. Opportunity cost.

To elaborate, even if g is perfectly equally useful in all geographic regions, if other selection criteria vary you can still get pretty strong selection pressures that effect intelligence (say something as simple as heat regulation of the brain or say a different rate of babies surviving birth in regions where fewer parasites are adapted to humans). Pleiotropy also means that these sorts of things may not always be apparent.

II. Speed of adaptation.

Also even given perfectly equal selection pressures on all dimensions, one would expect isolated populations depending on their size to adapt faster or slower to a new equilibrium (depending on which theories you espouse).