1. For readers who'd want to be more familiar with "tsundere": 'Kugi-type' is the word I used to categorize tsundere character who have been voiced by Kugimiya Rie (i.e Aisaka Taiga, Louise dela Valliere). Of course, the characters are distinct enough from each other but there share a certain vibe to them. Also, I think tvtropes has a good page for tsundere, I think it categorizes 'Kugi-type' under "Harsh".
2. It seems that I'm not remembering the story as much as I want. The part I remember the most in this case is that 'weight loss' chapter, and I already stated what I thought of it (whether it is "right" or not). Realizing that I'm not remembering much of Erika being "down", it makes me curious about what other people think about this: "What if Erika just over-thinks sometimes?" and "What do people think of Erika as an 'actor' and not a 'victim', in this case?"
Um, allow me to finish up clarifying point number 2 as much as possible since I wasn't being clear enough. (i'll be out soon, really ^^) I reread the weight chapter the most recently, so I'll go with that one too. Kyouya's words just tend to impact Erika deeply. She seems to accept everything he says, so her mindset literally has devolved to this idea that she has to "earn the right to be a human being" from a "pig".
She thinks it's only /right/ for her to be called a pig, and that she has to earn his love by being absolutely perfect, meanwhile she's constantly trying to accept him for who he is. That's double standards, and a huge power imbalance. Erika has an indomitable fighting spirit, so she'll try to challenge against being called a pig. But you know, I think you're right that it's not really that big of a problem, since Erika is aware that the latter half of the conversation was teasing, even if the pig remark was given and taken in full seriousness.
Anyway, I think that this is meant to show that Erika really wants that 'threat' (Kyouya's love) hanging in balance to challenge herself deep down, but with real people, that kind of comment can just hurt and affect self-esteem, and a relationship with that kind of extreme conditional love probably would feel more like a burden than encouragement. Erika IS Erika though, so i guess that's actually fine, and though the dog comments aren't meant to be taken in full seriousness anymore (?) Erika's still constantly being placed beneath Kyouya where she has to earn his respect and love. The "down" comment was just a generalized one (i use iirc when I'm trying to say i'm not sure if i remembered it right).
I feel the need to clarify to any viewers also that I don't think this manga is all bad in what it depicts. The author does try to be positive in terms of what they're depicting tbh, like showing that Erika doesn't need to act chaste and girls can want sex too. (iirc) Since it's a problem in society where girls are expected to be innocent and not have any sexual desires lest they be seen as debauched. I don't think Erika and Kyouya's relationship is that terrible either. Kyouya just goes over the limit and she shouldn't have to put up with it or be expected to in a real relationship.
Anyway... with all that said, I feel like I could still be wrong in how I'm viewing this too.