In Spain, the shops are open all morning, then close for a few hours in the afternoon because everyone goes for lunch and/or siesta. They re-open around 6pm or so and are usually open till 9-10pm after that. The only shops that are open in the afternoon are the ones run by immigrants. El Corte Inglés is also open all day. So don't schedule your shopping trip for the afternoon, shop in the morning or early evening.
Even if your interest about animals is only collateral, visiting the colorful pet market of Alfalfa Square is a powerful and intense experience that I strongly recommend. The combination of the bustling activity of the market, along with the soft spot I have for animals, made it one of my fondest memories from Sevilla. The market takes place every Saturday morning.
You can check out some snapshots of the market in my travelogue
Every Thursday morning and early afternoon, there is a market on part of Calle Feria. You'll find mostly clothes, books, antiques, and other second-hand goods. The antiques will probably cost you more, but I bought a white cotton skirt and pink embroidered scarf for a grand total of 8 Euros. Also, if you'll be in town for the April Fair, you might find be able to find a dress there for a fraction of the price in the boutiques (though the ones you'll find at the market are usually out of style).
While in Sevilla, you definitely should not miss the chance of getting lost (but with a map in your pocket, if possible) in the narrow streets of Santa Cruz district. Apart from tourist souvenirs shops and overpriced bars, the neighborhood houses the workshop of many local craftsmen.
Many times (but not always) in supermarkets you need to wait for the attendant to pick your fruit. Unlike in the U.S. you can't always reach out and squeeze that tomato or plum to see if it is ripe. You can, however, ask that they pick out a certain piece of fruit for you if it looks good.
What do do when the person at the checkout counter of the grocery store tosses a few plastic bags in the direction of your groceries? Put your stuff in a bag, of course! Unlike the U.S. don't expect anyone to come by and bag your groceries for you. You're expected to pack them yourself in most any supermarket so the checker can move on to the next person in line. Likewise, you are expected to take all of your groceries out of the cart or basket and place them on the conveyer belt for the checker to ring you up.