If I convert my checkpoint file (.chk) to a formatted checkpoint file (.fch) using Gaussian 09, and then convert it to a .wfn file using Multiwfn, does this process cause any difference in the final results of the AIM analysis? Also, does the Gaussian version (09 vs. 16) affect the results

This doesn't lose accuracy for topology analysis. However I suggest directly using .fch as input file of Multiwfn.

I don't know how did you prepare your present wavefunction file, however, as you can exactly reproduce the example in Multiwfn manual, the commands you inputted in Multiwfn should be correct.

I repeated the example from the file 2-pyridoxine_2-aminopyridine.wfn taken from the Multiwfn 3.8 manual. With this example, I obtain the same results for the critical points (CP), like position (Bohr), density of all electrons, etc., as those shown in the manual and with VMD.

However, when I apply the same procedure to my own molecule, my results differ from those provided by my professor.

Could you help me understand why there is this difference?

Thank you in advance!