Is it possible and safe to walk a long section (a few hundred KM) of the Silk Road independently?

Walk along the way must be a challenging thing to do.
You'd better to find some companies and prepare enough hiking equipment before starting off.

In addition, there are several ancient and civilized cities along this route, such as Xian, Lanzhou, ang Urumqi. If you have enough time, all of them are worth to tour around. :)