In relation to Mai’s past causing her friendship with Sayuri, that’s definitely why they are friends. That’s also why Yuuichi is their friend too. Sayuri implies they all have very similar pasts. In a nutshell they’re all people who face their past without actually accepting it, and think little of themselves in relation to others. It’s always that they are the problem in a situation. This was highlighted with the “I’m a burden” choice made by Yuuichi, where he decided to raise himself up to the pedestal he places Mai and Sayuri on.
I do agree that they’d become friends anyway. Mai still has a nasty past, even without the hunting stuff. They both had that moment of presenting something to a family member, and then watched that person vanish.
Mai’s death being a follow up of the “because I love you” line is actually fitting with the spirits’ behavior. They got riled up when Yuuichi was around. They would constantly distract Mai with noises and then go for Yuuichi while Mai was gone. They focused Sayuri whenever she was around. These invisible threats never really attacked Mai. They never really hurt Mai. Mai hurt herself, and these spirits hurt Mai’s friends. She’s trying to keep people away from her, though I don’t think she knows that early on. I do think she had this partially figured out later on. By the end I don’t think she believes the demons are anything more than something she wished for.
About Mai’s control of the spirits, it’s mentioned that she’s in a fight with her emotions. That’s very true. The most time she spends having fun with Yuuichi and Sayuri, the closer she gets to them, the stronger and more present the spirits should become. For an example, during the ball scene we see the spirit appear in a large crowded light-up area, something we hadn’t see them do before, and it was during the big night where Yuuichi focused all his efforts on making Mai “cute.” They always appeared to break the positivity.
Also, I gotta ask, how do you feel this route compares to the anime adaptation? I’ve noticed a lot of anime-only watchers completely miss the branch between reality and dream.