Does Italy use the chip/pin method for debit and credit cards? If I have a debit card without a chip but I have a pin, will it work?
1) Yes, all Europe uses Chip and Pin.
2) It should work in cash machines (ATM), and wherever there is a human being who knows how to use old fashioned signatures. Where it most likely will not work is unattended ticket machines.
Chips still aren't required for ATM machines, to take out cash. I used my ATM card (not even a debit card, no chip - just a magnetic strip) in Italy (and France and Slovenia) in May at several ATMs without issue anywhere. I used my chip and PIN credit card elsewhere, at ticket machines at the train stations. But my chip and signature (no PIN) credit card worked in most places (except train station ticket machines) anyway - that's the card I used mostly of the time because I get better rewards from it.