You could take bus no 919 from Deshengmen station to the Great Wall and the Ming Tombs.
There is no such 7 or 8 days smart card, you could purchase one from the subway station or other selling sites; if you will use it many times one day, you’d better deposit more money.
Besides, there are many hotels near to the subway station, ranging from five star to two star in different area.
Both the shuttle bus and airport express are available from the airport to the city center; the transportation depends on your preferred hotel location.
As for bottled water, it depends on what you want to choose. The price is different from different brands, the 500ml-600ml bottled mineral water is CNY2.00, which is cheapest one.