We will be arriving in Rome on a Sunday. Can anyone tell me what will be closed?
No. Most things will be open. It is Monday when a lot of the tourist sites are closed especially if open on Sunday. Only way to know for sure what is open and closed is to check the individual web sites.
The Rick Steves books contain a chart with a "Daily Reminder" in the section called Orientation that tells you the major sites that are closed on any given day.