Ok, I am not very familiar with these areas but questions I have so I can find the answers for you is:
1. Where did you get this information and 2. Do you have any records to prove it?
Thats probably the single most important thing - proving your info with sources. Next, have you taken the time to chart this all out and see exactly what you have? You start with yourself and work backwards filling in whatever you know. Then you need to start looking for sources..Have you the military papers for your grandfather? It will confirm his birth date, birth place and provide his parents names. You can get this information from the State Archives in Italy by just sending a request.
Ancestry has some Belluno records available as well/ Do you have a subscription?