I haven't been in Rome on a Sunday but I know in Naples and in Venice most of the regular businesses are closed on Sunday. Some of the tourist based shops stay open but not even all of them. I wouldn't plan on doing a lot of shopping on Sunday in Rome if I was you. Sorry to be the bearer of bad news.
We are going to be in rome from April 7 through the 10. The 9th is Good Friday. Anyone every been there over easter weekend? What can we expect in terms of crowds, businesses being closed Etc? We where thinking of taking the train south to Naples/Pompeii that day to get away from Rome but didn't know if things would be open.