Visa Information, please help me!

Hello,

I would like to go to Xinjiang province from Kyrgyzstan and then travel through to Beijing from which I will take a plane back to the Czech Republic. I want to get there either by Irkeshtam Pass or by plane from Bishkek to Kashgar.
I fear, that I will not obtain Chinese entry permit when I put Xinjiang into my itinerary because it seems the Chinese are a bit touchy about this region. I read that you should not mention travelling to Xinjiang during the application and that you must enclose return plane tickets. But if I plan to enter from Kyrgyzstan I have a problem with enclosing my ticket to mainland PRC since I will either not have any ticket or I will have the ticket to Xinjiang.

1) Is it possible to cross the Kyrgyz/China border by foot? Or to travel by plane from Bishkek to Kashgar?
2) Is it possible to obtain Chinese travel single-entry permit when I enclose 1 plane ticket from Bishkek to Kashgar and 1 ticket from Beijing to Prague? Or would I get a tourist type with just one plane ticket from Beijing?
3) Is it possible to apply for my trip without booking a tour to Xinjiang at Chinese travel agency?

Thank you
Andrea