Opening hours of shops in Rome are quite mediterranean: They rarely open before 9am but stay open until 8pm or longer. Between 1pm and 3pm some shops that are not directly in the city center close their gates. While most shops are open also on saturday afternoons, most shops not located in the city center stay closed on sundays.
Restaurants usually serve food between 11am and 2pm and then again from 7pm to 11pm. In the afternoon on the other hand it can be hard to find places that are open sometimes.
Many museums close their gates on mondays.