You don't have to know any Italian! I hadn't taken any Italian classes prior to studying abroad and I knew maybe three words total before I went over. You will have to enroll in Italian classes through AIFS while you are studying there, but you need no prior experience with the language.
Do it! I spent a summer in studying Art History in Perugia (about 2 hrs south of Florence) and didn't know a lick of Italian. Particularly in a place like Florence you don't need to know much Italian to get by, other than learning how to order gelato. While you're there though you should definitely take a language class. It helps make the experience more authenticate and memorable.
Yes, this program is open to seniors.