How do you handles talking and social situations in Masks which lock “persuade” move as an adult move?
I’m mostly interested how do you handle such situations at the table and in game mechanics. How do you avoid “just talking for 20 minutes without any conclusion”?
Do you talk for a some time and then offer player some compromise? (GM move “make them pay …” “tell consequences and ask”)
Do you go to meta discussion - they will agree if you … ?
My take has always been to let the convo go for a bit, until we get to the point where we can see that the PC’s pushing for something. If I see this, I can break in to ask for intent: what do they want from the convo. If it seems reasonable that the other party would agree, I do that. If it seems like they’re pushing for something the other wouldn’t agree to I say that they don’t-- but if the PC wants to keep pushing they can go to a Provoke move. The idea being here that the kids aren’t that great or subtle at persuading, and when they go down that path they approach it in a brute force way, even if they don’t mean to.
That’s exactly how I read the rules. (I can’t say “That’s exactly how I do it”, because I haven’t run the game yet).
You can also call for a “Pierce the Mask”, because that has the question “how could I get your character to …” or “how could I gain Influence over you”.
You’re absolutely right to remember that a GM move is “tell them the possible consequences and ask.” If players are trying to wheedle something out of an NPC without provoking them, treat it as a golden opportunity to make that move. “Yeah, seems likely the Silver Scorpion might give you access to the Exemplars’ training facility, but she’s going to be watching you and judging your technique the whole time. Are you up for that?” If they are, that’s an invitation to shift their Labels, which helps create more fiction whether they accept it or reject it. 
Yup, all persuading done by the teens falls under Provoke. The idea is that they are young and inexperienced in life, and don’t yet know how to gently persuade someone to do something. If they’re forced to try to convince someone, their only option is to threaten, tease, cajole, embarrass, insult, etc.