Since both countries are part of the Schengen area, the Italian visa is suitable for visiting Malta, as for any other country from the list of Schengen members. If the rule of the first entry into the Schengen zone is met - there are no visa restrictions for such a trip.

Yes, it is possible, if the validity of the visa and its multiplicity are allowed (in case the tourist has already traveled by it).

More information about the rules for entering the country can be found on the page "Visa to Malta."