Thanks for the fix.
For the second battle, I have a feeling the story is supposed to progress no matter who wins, but I won on my first try.
The third battle is indeed an optional victory battle. Even with the cookie, which can be used before a fight, I feel like the enemy's damage wasn't reduced that much and it took me several attempts to win. It's possible on the hardest difficulty with regen effects and Rin's speed buff. Sadly, Rin didn't confiscate the boss's weapon for her own use.
Edit: I beat the demo and did as many events for the party members as I could. Hopefully, this doesn't lead to a yandere ending if I try the same thing in the full release.