I need to quit my hangwon job after what will be 7 months due to family issues back home.
I think your boss will be disappointed that you're leaving, but happy that you aren't just pulling a midnight run, and actually giving the 2 months notice reuired in your contract.
In terms of paying back your inbound airfare, that's a contractual thing. Most of the EPIK, GPIK, SMOE contracts have a "if you leave before 6 months, you have to repay airefare" and a number of hogwans have followed suit.
Read your contract. If there's nothing in there about repaying airfare, you're fine.
You'll really just have to refer to your employment agreement. Those terms are agreed upon by school/teacher at the time of negotiation.
Also, from how I read your post, it looks as if you haven't fulfilled six months. Technicalities may require the six months of service before notification of resignation.
You don't have to wait six months to resign. You can resign on your first day if you want to.