I guess an intuitive arguement for why the gravity should be nonzero is to consider the limit as the major radius gets bigger and bigger. When it is very big, for a person on the surface it seems as if you are standing on the surface of a cylinder (the rest of the torus is far away), so you feel some gravity. So it can not be identically zero.
Note, though, that the analogous argument for gravity inside a sphere doesn't work: make the sphere very big and stand at some point on the inside. You'd think that you'd feel the same gravity as you would due to an infinite plane (constant g toward the ground), but in fact it would come out to zero because there's so much distant mass in other directions (the r^2/r^2 argument I made earlier). So it pays to be careful!
Yes. But standing inside the sphere it is kindof intuitive that the far-away parts of the sphere are not negligible---they fill up the entire night sky!