For the beginning of the year They're singing 「一月一日」("Ichigatsu Tsuitachi", "The First of January"), a traditional New Year's children's song. Good explanation with videos here; old-fashioned translation here.

I wonder if it's fuddy-duddy to spread a picture of a treasure ship under my pillow, even though I'm in middle school and I'm a devil... Edo-period tradition for the second night of the year to induce pleasant dreams and good fortune.

No...if anything, because I'm in middle school...I should value traditional matters... even though I'm a devil.