The fastest route is Milan-Brig-Zermatt. Check the timetable here: www.sbb.ch/en.
No, the SwissTravelPass is not giving free travel nor a reduction in Italy, with the exception:
When travelling from Milan to Zermatt via Brig, you must have a ticket from Milan to Domodossola. From there, your STP is covering the rest of your trip.
TripAdvisor Switzerland forum or MySwissAlps provide both excellent travel forums where you get further help on planning your Switzerland vacation.