Karl,
The GE should be driven down to ground level, if you drive below ground make sure the connectors are direct bury rated and remember where they are because the local AHJ might wish to see the connections...physically.
On the GEC connecting the (2) GE's their is really no depth issue on that except to ensure it is not subject to physical damage....we always bury ours down 6 inches between the (2) GE's....this ensures less chance of damage.