The way Peach and Perry got to Wavy Beach from Fury Volcano.
- I am suspecting that the volcano might have erupted after Wiggler's defeat, so Peach and Perry got blasted to Wavy Beach.
Princess Peach was on her period throughout the entire adventure.
- I mean come on, it's obvious.
- ...Though it's been established that she was under the effects of the Vibe Scepter.
The two mysterious figures seen in Perry's dreams were Bowser and Kamek.
- Rampaging around and stealing mystical artifacts from old men seems like exactly the sort of thing Bowser would do. Not only do their profiles seem to match up (a big, fat, menacing guy and a smaller wizard with a hat and magic wand), but it'd also explain why Perry's backstory becomes an Aborted Arc; the player has already exacted revenge on them. The slightly different shapes they have in the dream can be chalked up to Perry misremembering.
- Problem with this theory: The two figures were taking orders from a third guy who was offscreen. Bowser isn't the kind of guy who'd tolerate playing second-fiddle to another villain.
The reason why Peach's emotions have a major impact in the game is because said emotions ARE literally worried about her well-being
- Peach is accompanied by Mario, Luigi and Toad in Super Mario Bros. 2 and Super Mario 3D World, so she can count on their help in those games. But here she's completely on her own, so her emotions, working from the nervous system, do their best to provide Peach the skills best suited for the upcoming events and situations. If there's another game where Peach stars a game solo, the emotions will likely lend a hand again (though by then Peach will be mature enough to use their powers in a less stereotypical way).