in Beijing for 17 days. Plz advise on shopping, cheap mode of transport, food and sightseeing.

First of all, it is suggested that a Beijing Transportation Smard Card, which could pay for subway (CNY2/time) and bus (60% discounts).
You could enjoy almost all of Chinese food in Beijing, of course as many as world delicacy. The traditional food could be found at these tourism area and Qianmen Street. You'd better refer to the introduction here: https://www.travelchinaguide.com/cityguides/beijing/dining.htm

As for shopping, what kind of goods would you like to buy? For fashion ones, you could visit Xidan. For featured ones, you could visit the famous Silk Street.