Shopping in the Barrio Chueca: Calle del Barquillo has many good small boutiques.
Shopping downtown: Gran Via, Calle , Calle Fuencarral.
Must see places are the Royal Palace, Museum, Thyssen Museum, Reina Sofia Museum, National Archaeological Museum, Sorolla Museum, Cerralbo Museum, , El Retiro Park, Basilica of San Francisco El Grande.
For trains: For : Downtown Madrid is the , which has many hotels, restaurants and stores.
For those making a day trip to Cordoba, the train station does not have luggage lockers but the bus station beside it has luggage lockers.
My personal preference would be to allow time in Seville by reducing time in.