Italian student visa

It depends !!!

First of all, have a look on your visa first. It valids for Schengen States? or just only Italy?? If it only valids for Italy, then no !!! If it valids for Schengen States, you can pass another Schengen states to arrive Italy.

Once you landed in Italy, you should have to apply for a "resident card" in Police office, or related authority. After you have got the "resident card", usually stuck on your passport, you become "European Resident", then you can travel freely within European Union, not only for Schengen states !

of course
already with ur hk passport u can visit schengen countries without visa