It's generally not the mall or department store but the individual stores within the mall or department store that might have rules. Generally you might see a sign right at the entrance or whatever. The "open" parts of the mall or department stores usually don't have such rules. But again depends on the establishment.

As for food, I generally don't see where that would be a problem, I see people take pictures of their food with phone cameras all the time. As long as there isn't flashes going off and disturbing other eaters I don't see a problem, but again, keep an eye out for signs.