I puzzled together the following - very rough - itinerary. It kinda zigzags through China, hopefully including the nicest places. I know that travelling can be time-consuming, so that's why many destinations have more than 2 days allocated to them. I hope to do some of the travelling at night as well.

2d Beijing
2d Jinshanling (also accounting for the trip back to Beijing to get to the following destination)
3d Ningxia
2d Badain Jaran Desert
2d Gansu
2d Xian
1d Huashan
2d Henan
4d Qinghai
4d Kashgar (how do I get here?)
10d Tibet (too long?)
2d Litang
2d Sichuan
2d Chengdu
2d Zhangjiajie
3d Guizhou
2d Beijing

There are 2 destinations that didn't make the schedule; Yunnan and Guilin. I'd also like to hear if you feel that one destination on my list could be swapped for one of those. I'd love to hear any other remarks as well!

It is hard to assess. You put 2-3 days for places that are provinces. You could spend a lot more than 2 or 3 in Gansu, Sichuan, Henan, etc. There sure is a lot of moving around. You will waste a lot of time sitting on trains or planes.

My idea was to visit one place per province, that's why I put 2-3 days for those. But good point, I'll rethink that.

Concerning wasting time on trains; I think it's part of the experience. And night trains are hardly a waste of time.

Seven weeks?

It's ideal. Have only the vaguest plan. Book nothing in advance. Adapt as you go. Stay longer in places you like. Move on more quickly from those you don't. Change your mind when you meet people you like and head off to somewhere they've told you they enjoyed. The single biggest advantage of independent travel is flexibility, and except at certain very limited times of the year it's just best to make it up as you go along. There can be unexpected hiccups, and any itinerary planned down to the last half hour is going to fail anyway. Overall, your itinerary has the same frantic pace as that of someone with only ten days. Booking anything in advance from overseas significantly raises your chances of paying far too much.

There's little to say about the rest. You haven't said what you like. You haven't said what time of year you're travelling. Six of your destinations are either entire provinces or autonomous regions--where exactly were you thinking of going there? What can be done in a whole province in two days?

Some random thoughts:

Now is not the best time to be going to Kashgar due to the heavy security situation there (widely discussed in newspapers). You're also looking to travel across an area about the size of Western Europe to get to one small town which in recent years has been massively rebuilt and its population massively repressed since its original freewheeling market days. For now Dunhuang is probably as far west as you want to go (and you should want to see the Mogao caves), and if in Gansu then avoid Lanzhou but consider stops in smaller towns like Zhangye or Wuwei. Add Maijishan, not far west of Xi'an, if you can't make it to Dunhuang.

Add more time in Xi'an.

Add some time in the countryside. It's hard to tell with these whole province selections, but there doesn't seem to be much of that.

Points for including Ningxia, to which almost no one goes, but the Badain Jaran Desert is a made-for-tourists experiience to be avoided.

You'll have trouble entering Tibet and just going where you like. Regulations change all the time but you'll need to arrange a tour group, typically by cobbling one together with people you meet in Chengdu who want to do approximately the same thing.

Put either Tibet or anywhere in Xinjiang on your visa application and you'll be denied. So don't.

But most importantly, just put together some general idea of direction--an anti-clockwise loop, say--or a list of a few truly key destinations and make up the bits in between as you go.

I have to admit that I would find it frustrating to spend so much time in transit for so little time actually visiting anything, but maybe your experience would be different.

I spent 4 week just in the north of China; you might find some useful information or ideas in this old trip report:
Thanks for helping make my trip to China amazing!

Hope that helps!