Responses

I'm pretty sure Handa would recognize his own father. He did see pictures of the guy on Sensei's phone. And besides, the sensei last saw her brother eight years ago. Handa is in high school. So no, it's clearly not incest because Bro-con sensei would know if her brother had gotten married and had a child in the eight years before she lost contact with him. :P
It's incest because the sensei loves her older brother. And the student decides and is okay with the sensei calling him onii-chan. I'll stick around to find out what happens in the end.