"My mom was whore"
"Does that make me a bad person?"
Two completely different contexts and characters.
Not necessarily, given that August is potentially trying to reconcile with his daughter, and unlike sex-obsessed coomers he has enough common sense to realize said daughter wouldn't appreciate such attempt.
Maybe, but that's the first step. She meet one of the guy who basically run the Club. She's friend with Felicia, Hana, and Veronica already. The more people from the Club she spend time with, the more involved she is and the more risky it becomes. Especially when it's one of the people who runs it. Even if August don't do anything directly, it could lead to Mina meeting Kat, Chuck, and the other buttholes I forgot the name of. And well, I'm not going to go into a complete description of Mina's personnality, but knowing her, there is a high risk that she let herself be influenced, given the right persuasion.
So yeah, maybe not necessarely, but there's still a risk.