A great resource for you is
www.turbodieselregister.com.
To answer your questions...
What drivetrain does the 2003 - 2007.5 4X4 Dodge, Cummins diesel come with?
4 Speed Auto: Chrysler Corporate 48RE (I believe some 2003s came w/ the 47RE, Opt for the 48RE if you have the option)
Dana Front and Rearends: No, 2003 and up came with AAM axles. 9.25 (I think) in the front and 10.5 in the rear with auto in the 2500 and 11.5 in the rear with manual tranny or the 3500.
Which Transfer case: New Venture 272 Manual shift and 273? electronic shift
What issues did these have: None really... bent front axles if you like airtime... some driveline vibrations... death wobble on modified trucks.
What upgrades to they need: A good suspension... Lorenz, Carli, KORE.
Hope that helps...
Kyle