Regarding the meaning of high society/affluent people: just like most people, I directly thought of old money. But in her first course, she said there are different types of affluent people (tech, music industry, bankers, old money...)
So basically, to Anna, high society = rich. That's all.
So when she says she's part of affluent/ high society, it just means she knows rich people. Not that they have influence over a social group (too bad) or are well integrated.
Now why doesn't she openly clear this up you ask ? Because it sells more of course!
Regarding Lauren: it just shows what Anna preaches can work. Did it work for her ? That's up to debate, but given the fact she sometimes says one thing and then does another...