Center of gravity

I guess it depends on how you define interior. If by interior you mean where there is physical material, then the answer is no. Example - imagine an object consisting of three rigid rods connecting to be a triangle, with equal masses at each corner (think tinker toys). The cg is at the centroid of the triangle (in mid air). If you consider the interior to include the surface of the triangle, then the cg is in the interior. In the case of a kite, I think it depends on how long the tail is and how much it weighs.

Don't know if there is an easy answer why or why not. There is a mathemical formula (involving integration) to determine the cg of an object. The location of the cg is entirely dependent on the geometry of the object and the distribution of mass.