Can you use your ATM card to withdraw from either checking or savings in Italy as you can in the USA?
No choice -- all draw from checking.
No, there is no option to choose which account to withdraw from. By default it's from checking if the card is tied to checking and savings. There is also no option to transfer money between accounts.
One way around this is to sign up for your bank's home banking service. With it you can transfer money between accounts and track account activity on any PC with Internet access.
If you are worried about not having enough money in your checking, maybe you could set up "overdraft protection" with your bank. It would allow the bank to transfer money from your savings to your checking if you over draw on your checking. Talk to your bank about this. Every ATM we used in Europe withdrew from our checking. I don't remember being given a choice of withdrawing from Savings on the ATM screen in Europe.