I didn't meant they wanted to be romantically involved. I was just trying to prove they can see through her act.
Tardar said "Can anyone in that class see behind her mask, except Paku?"
About Ryuuji, Izumo just told him "tell me something I don't know", then he seems to get more serious and say "You'll drive everyone away like that". IMO these weren't empty words, but think what you want.
Rin did't think bad of Izumo because of how she treated Shiemi, I think he thought bad of Izumo because of how she was treating everyone, himself included. And he didn't changed his mind when he saw her crying, he changed his mind when she returned his shirt and thanked him. Also he's not interested at all in her past, but that's from chapter 53.