We did a tour of China a few years back and it was not quite what I expected, in a good way, but it is even more developed now with high rise flats. One down side was the number of factories we had to visit and you could only avoid going in one or two and everything we bought fell to pieces when we got home, but they were only little items so no big loss. As with the other stops which will probably be at some beautiful gardens or similar these shouldn't be a problem. The Wall may be a bit of a challenge but you don't have to go all the way up. The Terracotta Army are housed in a museum complex with lovely gardens and easy to walk round. The hotels were very good standard and I am sure you will be o.k. with the food, unless you are really fussy, and there are plenty of shops and the usual restaurant chains you'll find here.
We found the biggest challenges were trying to cross the roads due to the volume of traffic, ages sitting in the coach in the traffic jams on the roads which I think are worse than here and more polluted and all those sales people with whom my DH enjoyed bartering with.
You don't say what time of year you are travelling but we went early March and the temperatures varied greatly. Bejing was cooler but we were in t shirts, Xian was really hot, Singapore was very hot and humid. Perhaps it would be worth buying a little fan before you go.
Whatever you do and at whatever pace you go the tour guide will ensure you are accommodated. Enjoy every minute and I wish I was coming with you.