Does sublimation happen only on the surface or throughout the body?
The situation is akin to boiling.  If a molecule at the surface frees itself of its attractions to its neighbors, it can move into the vapor phase easily.  Same thing with evaporation at the surface of a solid.

Can a molecule evaporate from the bulk liquid?  The answer is no.  Imagine such a thing happening.  The escaping molecule(s) form a bubble inside the liquid.  The pressure inside the bubble is the vapor pressure of the liquid at that temperature.  But that temperature is less than the boiling temperature so the vapor pressure is less than the pressure external to the liquid.  The result is that the bubble collapses.  The boiling temperature is the lowest temperature at which the bubble pressure is equal to the external pressure.

Now think of sublimation in the bulk of a solid.  Here the "bubble" has to have enough pressure to break apart the solid.  It generally won't develop that much pressure.  Indeed, one can watch "dry ice" sublime well above its freezing point and nothing happens inside the bulk of the solid.

So the general answer is no, sublimation does not take place in the bulk of a solid.