kasdkashdkas

It's a bit more subtle (the corresponding statement for circles is not correct).

No, OP is correct; he spoke about an isotropic normal distribution (randn as opposed to rand).

Since the box is anisotropic, this would not give the uniform distribution (it's more likely to draw a "diagonal" direction than a coordinate axis direction).

They are only individually distributed uniformly in [-1,1], not jointly.

Near the poles the surface becomes very flat and therefore there is as much surface area in a slice of constant height than anywhere else. Archimedes was a clever fella :-)