It is relatively straight-forward to compute the center of mass for each face:
(By triangulating and computing the weighted average of the triangle positions, their relative face area being the weighting factors).
center_of_mass.blend (113.0 KB)
If you are interested in the bounding box, you first have to define a coordinate system in which to compute the box. You can look at this thread here to compute statistics per face in order to get a bounding box for every face: