You buy the 0$ paper and the alley gets unlocked. For Cains guilty plesure you ask Giuseppe in chapter 4. For the minigame, just click as fast as you can the bottom left corner.
Ah! thank you! I was also wondering about the math exam one, because I'm probably missing *something* but I've answered everything in every possible way but I'm still somehow getting it wrong. Is it hard to scratch this banner off on purpose?