I will say the tours are super watered down because of whitewashing history or because of poor translation, but they were still pretty cool to see. Don't carry anything heavy though, it is a lot of walking.
Didn't get to hit the Great Wall on my trip unfortunately.
In terms of food... I honestly can't tell you where I went, so sorry about that. Most of my trip I was pretty turned around. As you will see, Google Maps stinks over there. Mostly ate traditional Chinese food, which was usually great. I did enjoy eating at McDonalds once for breakfast but my hosts wanted to treat me to fancy meals every time. I'd be like, "I want to try Taco Bell!" and they would say, "You're only in Beijing once and you're our guest, you are not eating at Taco Bell." I'd recommend hitting a Hot Pot place. That was fun.
Super friendly people. I loved Beijing. Hope you enjoy.