Politzer’s Elementary Principles of Philosophy is the first ever book on philosophy I tried to read as a child: I found it in my parent’s bookcase and I was curious to know what philosophy was about. Even though I gave up very quickly, the first distinction it makes between materialist and idealist philosophy had left quite an impression on me. Seeing the title brought back some memories 
My very limited experience (I have been to China a few times for work, and managed to find 3 days to visit Beijing and 1 day in Shanghai):
The PRC was founded on the 1st of October, which is yearly celebrated: the first week of October is official holiday, and during the month of October it’s not uncommon for Chinese to travel around for their holidays. The positive is that you see lots of red flags around, the negative is that touristic places will be busier than usual.
I agree with others that your plan is overly ambitious, traveling from the South to Beijing sounds too much. Guangzhou is also very beautiful to visit, and I was told also the same for Xiamen (that others mentioned).
For Beijing (in case you are still adamant about going): I spent 3 days in Beijing and I couldn’t see much first because there is much to see but also because you need to book things in advance (not sure how much in advance, but definitely more than 1 week which is what I tried to do). Everything that you visit will have long queues, and also going from A to B in Beijing takes forever because the city is giant (I had 1.5 hour metro rides). If you do want to spend two days, the Great Wall would be 1 day on its own, I think it’s 100% worth it because it is something really unique (October is a popular time to visit it also because it’s the season that maple trees turn red so it’s very beautiful). The second day would be Tienanmen square, and the forbidden city? Beijing has also many museums and very beautiful parks and palace gardens, that you can spend a whole day there if you want (and are lucky with the weather), but with two days I think it’s very hard.
For food, I second what someone said about Sichuan cuisine, it’s great (but very spicy). I would also suggest trying a hotpot dinner if you haven’t had it before.
As others said you need WeChat and AliPay (and add a payment method in advance) and Amaps. For WeChat you need someone to activate your account I think, while AliPay you can do on your own. You can pay anywhere with your phone (with WeChat and Alipay), your credit cards won’t work, and you can also pay in most places with cash (at least that’s my experience) if you can get some before you arrive. Through WeChat and AliPay you also have access to taxis (I think they call it DiDi), and public transportation (but I think the public transportation you need to activate in advance). If you want to travel with the train, I would suggest the train app (Railway12306). You need to add your passport in the app, and after that you can book train tickets, and you can enter the train with your passport.
My experience is that most people don’t understand or struggle with English even in very touristy places, so you need a translator (deepL as others said). People are still usually helpful and friendly, so you do survive in the end. You do need a VPN if you want to stay in touch with family etc. There are travel e-sim cards that have automatically a VPN (they are more expensive than chinese sim cards but I guess it’s a convenience). If you don’t go for some travel sim card, I would suggest getting a chinese sim card at the airport.
I hope some of it is helpful.
When I visit my parent’s place I will look to see if I can find it again and give it a real read this time