Daikichi’s name means excellent luck, great blessing, etc. It’s the best fortune slip you can get in omikuji; you might have pulled it in the game’s 2017 New Year campaign. Obviously, there is no fortune slip that reads Subaru, which is supposed to be the joke.
Omen - 3
 秀越学園 ; It’s hard to guess how this school’s name should be read until they actually announce it. I’ll put Shuuetsu for now.
Foreign Enemy - 5
 Fine weather – you might be aware if you listen to the voice clips in the game, but yes, when Hiyori says “fine weather” (良い日和) or “foul weather” (悪い日和), he is saying his name. It’s a pun since Hiyori’s name (日和) means weather. I’m not sure how other translators do it, but I’ll just translate his catchphrase normally.
Exchange - 5
 Ohii-san. おひいさん. Basically “princess”; Jun should already explain it in his story that he refers to Hiyori as this as an attempt at sarcasm. As is with Mika’s Oshi-san, I can’t decide whether to translate it, so I’ll leave it as is for now.
Cheers - 3
 Kishoutenketsu (起承転結). Four act narrative structure developed out of Korean, Chinese, and Japanese traditions.
This isn’t important, but I just noticed after this chapter that Subaru refers to Hiyori as Ohii-san as in おひ～さん which is a tiny bit different than Jun’s おひいさん, haha.
Aside from Prologue, Monologue and Epilogue, all of the chapter names are actually two kanji words, though it’s difficult to carry over to English. “Cheers” (the wording I choose might be confusing, but it’s cheers as in when you toast) in Japanese is pronounced kanpai (乾杯) and it’s a homophone of “total defeat’ (完敗, kanpai), which is… what Trickstar experienced in that chapter. I didn’t mention it before because other chapter names might be wordplay I’m not aware of too, and it’ll be strange to just point out that one, but oh well.
Kiseki series is written in katakana (キセキ), but in the event name (輝石☆前哨戦のサマーライブ), kiseki is written with the kanji for pyroxenes (輝石), and separately these kanjis mean sparkling (輝) and stone (石).