Hi Bebo - for a polygon, you can do this with Inset in the V7 WIP. To create surfaces you can do this in V6 with the Gumball:
DupBorder your surface (or make say a rectangle as a curve)
Select it.
With Ctrl down, start dragging the Gumball plane icon in Top:
to invoke 2d scaling.
Press Shift at the same time to convert 2d scaling into extruding
However there is not a way to quickly ‘subdivide’ a V6 surface in the way that you describe. V7 will have sub-division surfaces, these are partially implemented in the V7 WIP builds.