Thanks. I'll add some copy to the front page to clear up some of your questions.
Payments are all done through Stripe Connect. Right now Teachity isn't taking a cut, but if the site ends up getting enough users then I'll start experimenting with pricing... as a comp, I think airbnb is 6-12%, elance is ~9% of each transaction.
Refunds are tricky. Everything is run through Stripe so I can't directly issue refunds above Teachity's cut. If people have a really horrible experience/no-show tutor I can ban the tutor and give refunds out of my own pocket although that wouldn't be sustainable. I'm working on a feedback system, so hopefully that will head off most problems... although you need enough reviews for that to be effective in the first place.