You're better off paying for a direct flight here. Air China has non existent customer service.
I did a day trip with a tour agency which crossed the border. It was OK if you're not clued up on Visa requirments and would rather have it taken care for you
U can go Shenzen on a 5 day visa which u get at the border for £30
You can easily DIY it, we've booked most DIY including trains, accommodation etc the only thing we may have to do a tour for is hiking in the Altai/Ogli region in Western Mongolia, although we may have to adjust this as the Eagle Festival is on when we are there so the flights from Ulaanbaatar to Ogli are super expensive.
How awesome. Will be amazing. I really want to do this but been told not to do it alone & I am not into organised trips but may have to for this one. Have a fantastic time