If it is shifting fine, I wouldn't do anything to it. If it is not shifting fine, do a fluid change and make sure you change the filter. Has shifting changed recently?

Don't worry about GM Powertrain. The shifting characteristics were determined jointly by BMW and GM Powertrain. It shift firmly but smoothly.

The 3.0 does not have a ZF transmission. Follow the tag on the transmission, but I expect it was Dexron III, now upgraded to Dexron VI.

Diffs aren't a problem to do.

Transfer case is similarly straightforward. It isn't x-drive, so I believe it is Dexron again. No computer reset required.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue