Should I bother using short int instead of int? Is there any useful difference? Any pitfalls?
What Ben said. You will actually create less efficient code since all the registers need to strip out the upper bits whenever any comparisons are done. Unless you need to save memory because you have tons of them, use the native integer size. That's what int is for.
EDIT: Didn't even see your sub-question about const. Using const on intrinsic types (int, float) is useless, but any pointers/references should absolutely be const whenever applicable. Same for class methods as well.