1. You can try Beijing restaurant. Its off Salwa Rd. Al Mirqab Al Jadeed. Or Chopsticks at Grand Regency Hotel. Both restaurants serve authentic traditional chinese foods. I've not tried it personally, but it was recommended by a colleague....

2. Not sure if there's an outlet here in doha. But in your leisure time, try visit City Centre, Landmark or Villagio... There's some international boutiques there. Worth a try...