To stay on the Yumi topic, strangely, I never see any «love», at the beginning, on her part for Sensei.
For me, she's seeking for «attention», but a good attention, and not a physical one.
And she get it when Sensei «try» to help her getting a job. And, for me, that's the moment where a connection, and maybe some love, appear.
And when she saw Makoto with Sensei in the park, she wasn't jealous, but «envious». Because, at that scene in the park, what happen? Nothing. They aren't fucking. Nor kissing. They're barely just talking. (If my memory don't fuck me up again!)
All what Yumi ever wanted. Someone who can hear her out. Someone she can «trust». Someone who can be proud of her.
And, since Sensei isn't exactly what she need, but may be, she help him when he black-out. That's why she stay around when it happen. Not by «love», but with the hope that, if she support/help him, he might be able to support/help her.
Anyway, at least, that's how I see her.
Maybe I'm wrong.
Also, like all of the girls in this game, she have some insecurities. Maybe it's the age, but since I've never be a teenager myself, I don't know what's relevant or not.