It is true that motorbikes are forbiddend in the city center area. As for traveling, these tourist spots do opened during weekend, the opening hours are the same with other weekdays, but the shopping centers may be closed one hour later until to 22:00 in winter.

These department stores and supermarkets accept both visa and mastercard cards. Very safe for using. However, credit card is not accepted widely at another places such as bus, taxi and restaurants. You'd better take enough RMB cash.