Addendum: After looking online, I see that Meloetta and Genesect are not automaticaly included (one of the tricky bits with it being listed alphabetically instead of by Pokédex number). I'm still trying to figure out how the AR Viewer mode works too.
To unlock both of Meloetta's Formes, the player must create a quiz with the keyword of RGFOAUTF (Japanese version) or TTQALFHN (English version), and complete the quiz. This code will also unlock Relic Song in the Move Dex, Meloetta's signature move.
To unlock Genesect, the player must create a quiz with the keyword of QUHDPHEU (Japanese version) or PHSKUTDF (English version), and complete the quiz. This code will also unlock Techno Blast in the Move Dex, Genesect's signature move.
When the player gets perfect on all Challenge Mode quizzes, Hard Mode will be unlocked, allowing access to challenges 40-69. This can also be unlocked early by entering the password UJFPJGAD rather than completing all the Challenge Mode quizzes.
And it turns out there's an iOS version of the app for peeps who don't have a 3DS yet.