Re: THE WHAT.
The Doctor says he's there for the spectacle of the entertainment, and acts surprised if told about the sexual aspect of the club, but he's not as dumb as he looks. He's well aware of what the club is about, having been told by River, but is pretending so he can act like a goof.
Kurt? What can I say? I've always imagined he leaned toward the kinky side, into sex using harnesses and trapezes and stuff like that. He'll flirt like hell with the gymnasts who work there (ladies and gents), but even if he gets an offer, he'll decline because he doesn't want them to find out that his cool outfit isn't some sort of costume and makeup, but really him.
Percy... he's the kind of conservative, straight laced politician fellow who looks vanilla on the outside, but secretly has all sorts of kinky desires. Between his admiration of authority and his adherence to rules, he's ripe for B&D, being told he's a 'bad boy' that needs to be punished. Besides from any advertising or word of mouth, Percy would've known about the club from City Hall and dealing with the complaints and campaigning that didn't want it to open. Curiosity sparked, it would take a few days for him to build up the courage to go check it out, hoping that nobody recognized him. And yes, he would make an appointment to go into the back room. And yes, he is currently in a relationship with Zelda and is doing this behind her back, cheating on her.