interesting thoughts on nodoka, I figured she was laughing because her 'evil' plan for revenge on yumi came to fruition, the bathroom thing wasn't even the plan, the plan was to get her kicked out of school by provoking her in such a way she would have to retaliate. cant wait to see how she reacts that she is back in school again.
as for yumi's detentions...
she says what he did to piss her off in one of the events a long time ago and I think you see it in the "alteration" scene when its jumping around to different images of yumi at the end of the previous update.
he made her stand in a corner with her shirt open while he stared at her
pretty sure it was the bandaged breasts scene
right before the switch to this image
sensei says "you were an idiot for ever thinking you could trust me after all i've done to you and the most disheartening part of all of that is I can't even remember some of it"
the jacket is the old school uniform yes? before it was changed
i'll go back and go through and find which Yumi event it was and add it here