No, you don't need to know Italian. You'll learn some while you're there, though!
Yes they are! All of the courses at the Florence Summer Institute are taught in English.
One of the most important questions. Kent State's Florence Summer Institute cost estimate (located HERE) can give you a sense of the initial cost. Note that by applying for available scholarships (some only open to regional campus students) the cost can be reduced dramatically. You can also apply student aid to your Florence experience. Your advisors (academic and financial aid) can help you explore your options!
No! Students from other schools can be part of the Florence classes. See the link HERE about registering as a guest student with Kent State.
The U.S. State Department has a site which will help located HERE.
The city of Florence is quite compact. You can walk from one side of the city to the other in about 45 minutes, so the main way to get around Florence is by walking. There are trams available from the Florence airport and to other spots around the city as well.
The main way to get around in Italy (and Europe) is by high-speed train. They're faster than driving or by bus and can get you just about anywhere you'd like to go. They're also quite comfortable! You can purchase individual tickets or buy passes which are cheaper if you're looking to use the trains often. Here is a link to a video showing a typical Italian high-speed train.