Who's the person that Madeline calls in her dream at the end of Chapter 2? It seems like they knew Madeline very well, but they're never brought up again after this cutscene.
It seems like this was left intentionally vague, but we can speculate based on their conversation. The man calls her "sweetheart", so he may be Madelines father or significant other. He also says they havent talked for months, so they seem to have a strained relationship.
Considering that person's portrait and the way they and Madeline talk leave their gender also vague, it's probable the developers intended their identity and relation to Madeline something the player themselves projects. They could just be a friend, a significant other, a relative, and whoever the player takes them to be informs something unique and personal about Madeline.
The game's text database file refers to them as Madeline's ex.
Why is Chapter 6 the only one without any strawberries?
It's probably because there's a large chunk of the level where you have multiple paths that do not loop back, and would thus be unfair to have strawberries in. But that doesn't explain the start and end of the level. And they certainly weren't worried about disrupting the tone by putting strawberries at the end of chapters 2 and 3.
It's been theorized in Something Awful that the strawberries represent the mountain's challenges to Madeline. In Chapter 6, Maddie momentarily loses her interest in climbing the mountain, so its challenges mean nothing to her anymore — so no point in keeping the strawberries.
While it's clear that Badeline represents an aspect of herself that Madeline has been trying to suppress, I still can't figure out exactly which personality trait or emotion Badeline is supposed to represent. It's hard to pin down one specific thing that Badeline consistently embodies, unless she's just a broad manifestation of "negative feelings" in general, but that doesn't really seem right either.
It's never officially stated. She definitely embodies Madeline's self-doubt and anxiety, given how Badeline seems to genuinely believe climbing the mountain is impossible. Some other things she does, such as insulting Mr. Oshiro and her violent reaction to Madeline rejecting her, could be her suppressed or restrained anger. It's most likely Badeline just represents the parts of Madeline that she tries to ignore or hide, whatever they may be.
What happened to Madeline at the end of Chapter 8? From what I can gather it just seems like she stays there...
The fact that Chapter 9 exists means she does leave. Presumably she stays there for a little while, just enjoying being somewhere quiet and calming, then eventually leaves after a few minutes or hours.
Why are there dream blocks in Chapter 7? The only other places they appear in are Chapters 2 and 9. The only in-story explanation I could think of is Chapter 7 being a YMMV example All Just a Dream