Can I change my tires to a 265 R16 size, the actual original size of my GMC 2500 Sierra HD tires are 245 R16. My pick up have 6.6 diesel engine with an allison 6 speed transmition, and 2 x 4 configuration.

1st number is tread width (mm)265
r =speed rating
2nd is wheel size, in inches 16
the rule of thumb re tread width, is the tread should not exceed the inner wheel width,measured inside the wheel/tyre sealing area by more then 20mm.
otherwise car will tend to sway when steered for moose test.so check your wheels first...
r rating only good upto 100 mph intermitently...

Yes but check your speedometer with another vehicle with proper size tires .