Parodies, references explanations for Kaguya-sama wa Kokurasetai? Tensai-tachi no Ren`ai Zunousen / Kaguya-sama: Love Is War 2 episode 9.
Timestamps are approximate
2:30The sequence is a parody of the opening for the 1984 Japanese TV series School Wars ~Nakimushi-sensei no 7-nen Sensou~. The rugby part at 8:48 is also referencing School Wars with rugby being a central part of the story.
2:53 Shinomiya Kaguya in Iino Miko’s fantasy says “kusatta mikan wa hayame ni shobunsuru ni kagirimasu” (literally “rotten mikans (Citrus unshiu) are best disposed of early on”, and translated as “We have to get rid of the rotten apples as soon as possible”). It is possibly a reference to the Japanese TV series San-nen B-gumi Kinpachi-sensei / Mr. Kinpachi in Class 3B where delinquents were seen as “rotten mikans” inside a box with other students which would cause nearby mikans (other students) to also become rotten and therefore should be disposed of.
5:04The coloured text appearing on the background effect is similar to the next episode previews for the anime Higurashi no Naku Koro ni / Higurashi When They Cry while the overlapping voices is similar to the next episode previews of the anime Angel Beats!
18:28On the whiteboard is “moshikashite uchira… irekawatteru~!?” (roughly “could it be we are… swapped!?”) which is a parody of the longer lines said by the 2 main characters in the anime film Kimi no Na wa. / Your Name.
22:31The black text appearing on the white background is a parody of the next episode previews for the TV version of the anime Angel Beats! (in the disk release version, preview video of the next episodes are used instead)
Screenshot credits: ©赤坂アカ／集英社・かぐや様は告らせたい製作委員会