These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
The English title of the humming song is "I'm Human", which explains why Mechazawa likes it so much.
Kamiyama failing to notice Takenouchi, the largest human character in the cast, and ending up sitting on his lap as a result. This scene is like any other Out-of-Character MomentPlayed for Laughs until you notice that Kamiyama has his eyes closed for most of the scene. Kamiyama is the smartest member of the cast, so the scene may be a Deconstructive Parody of Eyes Always Shut, a trope often applied to wise characters.
Fridge Logic: Wait, why is Yamaguchi's first name (Noboru) written in katakana if there is a kanji symbol for it?
Memetic Mutation: It's become a running joke that every time anything Mechazawa related appears, people will post comments jokingly expressing confusion about there being something peculiar about that delinquent...