Does the time difference between Melbourne and Rome change during the year?

Yes. Because of daylight saving time the gap moves between +8h and +10h.

When is the best time to call Rome from Melbourne?

There is no overlap between standard working days, so one side has to call early or late.

Melbourne is 8h ahead of Rome. This gap is not fixed: daylight saving time moves it between +8h and +10h during the year.

Melbourne

Australia

--:--:--

Rome

Italy

--:--:--

A 9-to-5 working day in Melbourne does not overlap one in Rome at all — somebody has to take the call outside office hours.

City	Time zone	UTC offset
Melbourne · Australia	Australia/Melbourne	UTC+10
Rome · Italy	Europe/Rome	UTC+2

What is the time difference between Melbourne and Rome?: Melbourne is 8h ahead of Rome. This gap is not fixed: daylight saving time moves it between +8h and +10h during the year.
Does the time difference between Melbourne and Rome change during the year?: Yes. Because of daylight saving time the gap moves between +8h and +10h.
When is the best time to call Rome from Melbourne?: There is no overlap between standard working days, so one side has to call early or late.