1, Xinjiekou mostly belongs to baixia district.
2. Jingxi Hotel is located at the junction of Caochangmen Street and Jiangdong North Road and should belong to jianye district. This is not completely certain, because it is also close to Shimonoseki.
I don't know which bus can go through.
Taxis must be very expensive, and 30 yuan should not be enough.
5. Suggested route: Take Metro Line 2 from Xinjiekou to Yunjin Road or Jiqingmen Street, and then take the bus to Jingxi Hotel. Save money quickly!