What does "lead" mean here? lead an activity?
This evening, as on every Thursday night, psychologist Maud Lehanne is leading two of France’s favorite pastimes, coffee drinking and the “talking cure”. Here they are learning to get in touch with their true feelings. It isn’t always easy. They customers--some thirty Parisians who pay just under $2 (plus drinks) per session-care quick to intellectualize，slow to open up and connect. “You are forbidden to say ‘one feels,’ or ‘people think’,”Lehane told them. “Say ‘I think,’ ‘Think me’.”

1. psychologist Maud Lehanne is leading two of France’s favorite pastimes, coffee drinking and the “talking cure”.
What does "lead" mean here? lead an activity?
2. They customers--some thirty Parisians who pay just under $2 (plus drinks) per session-care quick to intellectualize，slow to open up and connect.
" $2 (plus drinks)"
Does $2 cover the drink or not?
3. They customers care quick to intellectualize，slow to open up and connect.
What does "care" mean here?

Question

What does "lead" mean here?   lead an activity?
This evening, as on every Thursday night, psychologist Maud Lehanne is leading two of France’s favorite pastimes, coffee drinking and the “talking cure”. Here they are learning to get in touch with their true feelings. It isn’t always easy. They customers--some thirty Parisians who pay just under $2 (plus drinks) per session-care quick to intellectualize，slow to open up and connect. “You are forbidden to say ‘one feels,’ or ‘people think’,”Lehane told them. “Say ‘I think,’ ‘Think me’.”

1. psychologist Maud Lehanne is leading two of France’s favorite pastimes, coffee drinking and the “talking cure”.
What does "lead" mean here?   lead an activity?
2.  They customers--some thirty Parisians who pay just under $2 (plus drinks) per session-care quick to intellectualize，slow to open up and connect.
" $2 (plus drinks)"
Does $2 cover the drink or not?
3. They customers care quick to intellectualize，slow to open up and connect.
What does "care" mean here?

Answer

Sue,

1.  I think you're explanation -- lead an activity -- is correct.  Lehanne is the leader in the room, to whom others look to direct the conversation. 
2.  I agree with Felipe's answer. 
3.  I think there is a typo in the sentence, and it should be "ARE quick to intellectualize" not "CARE quick."  "Care quick" makes no sense.  "Are quick to intellectualize, slow to open up and connect" means that these people are smart/brainy but tend to keep their feelings to themselves and not make friends quickly.

Answer

I'll try to answer your questions:
1. It means that she's on top when it comes to drinking coffee and talking, compared to other situations/places where you drink coffee and/or talk. 
2. They pay less than $2 per session, but they have to pay for their drinks. 
3. I think this sentence is wrong, I would replace it with "The customers care to intellectualize, open up slowly and connect.