We will stay at china world apartment Beijing.

Haven't found any noted muslim restaurants located in walking-distance from this hotel. But, you could find muslim food easily in other close area, such as Wangfujing and Qianmen. As for the imitation brand, just have a try at nearby Silk Street.
7 Days will be enough for you to tour around Beijing totally, covering these most famous attractions. You may refer to the suggested tour itinerary on this website.