Does Auschwitz be open on sundays in january?
Yes, Auschwitz is open 7 days a week, between 8am and 3pm in January. Have a look at auschwitz.org.pl for more info.
Dunno about hop on/off tours but there's a a good guidebook with walks that will give you an insight into the history of the City - it's called Krakow's Old Town, published by Bezdroza and availably from EMPiK (huge book shop) on the Rynek. As far as I know, Crazy Guides concentrate on Nowa Huta, not Krakow.
Main shopping areas are Ul. Florianska, Ul. Grodzka in the Old Town. There's also a huge shopping mall next door to the train station (Galeria Krakowska). Prices probably won't be as cheap as you might be hoping for though...