How could you determine the specific halogen like Cl, Br, I present in your test compound after fusion?How could you determine a specific halogen...

One way is that since each element emits a characteristic pattern of electromagnetic radiation, using the techniques of mass spectroscopy, every element in a given test compound can be identified by its unique pattern of dark lines in the spectrum.  Each halogen has a similar set of lines, but each set is found in a different spectral region, as these lines are defined by the distance electrons are from the nucleus and the energy levels of each electron.  These vary from each of the halogens (as they do for each element)  and can be used to identify not just a halogen, but every element in a compound.