All the problems you've described are well-known issues with that generation of GM trucks.
The instrument cluster stepper motors have been a problem from the get-go. They replaced the cluster on my 2003 back in 2005 under warranty, and it was fine, but I've heard that the replacements weren't always perfect. There are youtube videos showing how to replace the motors with aftermarket ones.
The transfer case is probably experiencing the well-known "pump rub" issue, and is also causing the "service 4x4" light to come on.
Your vibration may not be driveline/brake related at all. Take a look at the "frame beaming" issue. The cure is new hydraulic cab mounts. Many have chased driveline/brake issues to no avail, only to find out that it was "frame beaming" all along.
I had a vibration/shaking problem in my '02 last year. Turned out the front jounce bumpers were rotten and one was completely broken off. Drives like a dream now that I put new ones in, and it only took 20 minutes.