The situation of princes skipping classes did exist in the Qing Dynasty. According to the contents of documents [3] and [4], the princes sometimes skipped class. Even if the management of the study was strict, it could not completely prevent their mischievous behavior. Emperor Qianlong was not polite to such situations. Once the prince was found to have skipped class, he would severely criticize the teachers. However, the document did not mention the specific reasons or consequences of the prince skipping class. Therefore, I don't know the details of the prince skipping class.
Toge Inumaki is important too. His special cursed speech ability makes him stand out. Also, the principal of the school, Masamichi Yaga, is likely to be important as he is in a position of authority and has an influence on Gojo and the other students. There could be other characters like the members of different clans that also play roles in the complex web of the story.
"Rope Skipping Song" was a children's literature that described the story of children skipping rope, so it could be regarded as a children's song or nursery rhyme. This song was widely used in children's literature and became one of the classic songs for children to skip rope.