If she's crying happy tears over her ex's death that feels extremely fucked up and gross to me. Especially combined with the mental illness factor. I think it was important that they broke up, though I also think this story feels excessive in it's spite towards the ex and dealing with a partner that has mental illness.

It's a bit cold, but if you pay attention you'll also see that when she's with her new girlfriend is the only time she doesn't have bruises on her face, so...

I see the author saw Hibike and chose violence.

So what does Baiser mean in Magia Baiser’s name?

So far it looks to me like either kiss or Meringue which is a sweet dessert that is beaten stiff. Both seem to work in their own way.

In french, Baiser either means (as a noun) kiss or (as a verb) fuck.

I suppose the author went for kiss, but given the manga I'm not 100% sure.