Hey, Jenny. My recollection is that some shops close on Sunday, but others are open, almost certainly with shorter hours than during the weekday. The actual closing time of stores probably varies by season. Sure seemd when we were in Firenze in the summer more stores were open later--past seven, even--than when we were there in the winter. Regarding the variety of outlet malls that surround Florence...most can be reached via public transport by taking a brief train ride, followed by a brief taxi from the station to the mall. For example, checkout this page:
http://www.tours-italy.com/florence/outlet_stores.htm