The prime shopping area is right by La Scala. (Sorry, I don't know the subway stop but I'm sure others will.) Definitely a place she'll like although th evalue of the dollar rigt now may discourage her from buying much.
We found 2 years ago that public transportation to and from the airport is a little clumsy. We took a subway to a central subway station, then took a train from there to the Central Train Station (Mussolini-era; definitely worth getting outside and looking around). From there, subway transportation is fine. You can buy tickets at all the newsstands.