Hello...
The factory transfer case shift control is what's next to the radio. Top button rear locker, then 4HI, 4HI LOCK, and finally 4LO LOCK. If you're seeing another "locker" button near the gear shift someone probably put a front locker on the truck. EDIT: If the button is all the way at the bottom directly below the tow/haul button and to the left of the AC and OnStar, you may be looking at the rear air ride height adjustment switch...I think it has a picture of a truck with an up/down arrow near the rear. Those three buttons are TC2, Tow/Haul, and Height Adjustment (if equipped...if not the bottom spot has a blank).
Regarding what parts will cross between your '01 Burban an '06 H2, I think you'll run across a few. This would be a good starting point:
http://www.wholesalegmpartsonline.com/
You can look up a particular part in the GM inventory and at the bottom of the part's page you'll see "Product Fitment/Applications." If you expand that you will get a list of all the other GM vehicles that the part works with.
For instance, if you look up the Upper Control Arm (PN 25905442) used on the H2, the page shows that the same arm was used on 261 other vehicles (including the 1999-2014 Suburbans); but the lower control arm (PN 20832025) is unique to H2s. This site should help you answer some of your questions.
As far as frame dimensions go...I don't know off hand; but here's some images that might assist until you get some exact measurements.
2001 Suburban 2500 Frame
H2 Frame
