Most small shops in Barcelona open from Monday to Saturday from 9 am to 1:30 pm and from 5 pm to 8 pm. The larger shopping brands like Zara, Mango and H&M open at 10 am and remain open until 10 pm. And some smaller stores close on Saturday afternoons.
The shopping malls in Barcelona open from Monday to Sunday from 10 am to 10 pm. However, the Maremagnum shopping center is open on Sundays and every day of the year, including public holidays.
The museums in Barcelona open generally from Tuesday to Sunday from 10 am to 8 pm. Most museums and art galleries are closed on Mondays. There are of course exceptions like the Wax Museum and the Museu de la Xocolata.