Well I rather 'promised' to post a response to your post #3, so here goes. Others have posted really good responses to some of your main points, so I'll skip over those.
I am not completely able to tell where people are from in China simply by their accents.
Sorry, I should have put it another way: You can tell by the way a person speaks Chinese that they are not from your home area, and that's what happened with the cab driver. He guessed wrongly about where you came from, but he was right in guessing your accent was not local.
There is a rather confrontational undercurrent in your posts that seems to have an element of politics. I have lived more than 10 years in China and one thing I learned early on is to not discuss politics other than internal US politics with Chinese- the overwhelming majority are simply unequipped to do so. In the west we are at least aware that perhaps large numbers of people hold opposing ideas/opinions whether we understand them or not. We feel that debate is generally healthy to our democracy and our way of life. Chinese get always only one side of things and any opposition to government dogma is put down to 'a few troublemakers'.
You cited Wikipedia, which is generally a good source of unbiased information. I think that other users of this site should know that where I get my internet (Guangxi province), Wikipedia is blocked, so I guess it is for you as well and you use a VPN in defiance of your government's wishes.
I've searched the Internet before that many Western people claimed that they have been discriminated because of their accents.
Marketing research has shown that human beings are far more inclined to complain than they are to say they are happy, and the internet has provided a convenient platform for all sorts of gripes- legitimate and otherwise. "Many people claim..." is the weakest of arguments. We have an idiot for a president who uses that all the time in his speeches. "Everybody is saying..." "People tell me..." "I hear that..." are all ways he tries to legitimize the things he makes up. Certainly, there is discrimination based on how people talk, but it's not only about their accent- it's more often really about what they say than how they say it. Heavy accents tend to go with/come from poor education, and it's often convenient to blame something beyond ones control rather than to take responsibility for improving one's lot in life.
... it is undeniable fact that there is still racism in the West as well as in the USA too.
Yes, it is true but, as I stated, we are learning to do better, and I like to think that progress has been made, though we have been taking steps backward since 2016. There is great shame in our national past. But only by facing those facts and talking openly about them can we make real progress, even if that progress will always be too slow. The debate about what best to do about it continues, despite the efforts of our current 'leadership'.
And I believe classes are still important in the UK, and some other European countries.
It is the same everywhere. How many Chinese movies are about some poor boy/girl who works very hard to get an education and improve their situation in life?
So [some?] British people, if not all, are interested in the royal family.
Sticking my neck out a bit here, but I think most people in Britain think of the royal family somewhere on a scale from disgusted to amused to tolerated as a somewhat-useful tourist attraction to celebrity worship with the vast majority somewhere in the middle of that scale.
Many British politicians actually are from the upper class.
I think that many is the wrong word. There are hereditary positions in UK government, but they are in the less powerful branch of Parliament. If, by "upper class" you mean ambitious, well-educated people, then I say, 'Of course- aren't those the people we want in charge of government?'
American movie named My Fair Lady produced in 1964 tells how accents were important in England. Why did the haughty professor fall in love with the humble florist? Because that's how movies work!
Why did she finally become a fair lady?
That question was only addressed very late in the story. Neither Eliza nor the professor really thought about that in the beginning. The professor thought of her as a purely academic challenge and she took a gamble on (at least temporarily) a better life that included central heating and chocolate.
Would you say the change of her accent was not a factor, even if it would have been a minor factor?
No, but that's a bit like saying Cinderella married a prince because of her shoe size. The message of the story was/is that love finds us when/where we are least looking for it and despite societal boundaries.