Didi is pretty popular, you can get it in most cities, though it really depends on how the regulations are being enforced at the time (didi in Beijing and SH can go away for a few days when there are crackdowns on black cabs). As for rates, check out:

https://ride.guru/estimate/Zhongguancun,%20Haidian,%20Beijin...

That is my standard trip from work to home when I lived in BJ. Didi was just 1.3X more than a taxi, though I usually just took a taxi because wepay wasn't friendly to foreigners at the time.

Prior to this new fundraising round Uber took a 17.7% stake in Didi in exchange for handing it's China assets over to Didi, which was worth something like $6 billion. So even though Uber lost in China, they actually kind of won, unless, I guess, they decide to start fighting again in some other market.

https://www.bloomberg.com/features/2016-didi-cheng-wei/

it doesn't have competition, they control more than 90% of their market, similar with Wechat having monopoly on IM, so it's not like you have choice no matter what's your age

my personal experience with didi was very inconsistent, half rides were ok, half rides were horrible experiences, so next time i would just call straight taxi company to get regular taxi (yes i am aware you can order regular taxi through Didi, lived in China for years)

Yes, Didi is universal across the country. You can order Didi through WeChat and actually what you get is a regular taxi car, not a Uber-type freelance driver.

you can choose if you want regular taxi or black car, it's up to you, you can even choose shared car with other passengers

This is going to vary massively city to city, just as it does for Uber/Lyft/Grab in other countries.

Sure but there are reports and research. Here is a site that aggregates this data.

http://uberestimate.com/prices/San-Francisco/