Much of Dia and Kanan's actions before they joined makes sense when you take into account their shared school idol background with Mari.
Despite the fact that Mari's family has a lot of money, it's still weird that a student gets appointed as the new director. However, after we get to know that Uranohoshi is closing, it makes sense: naming a 17-year old student as director, one could attract some media to the school and hold off its closing for a year or two.
The performance of MY Mai TONIGHT brilliantly combines the ideas of the 1st years and 3rd years from Season 2 Episode 2.
The song prominently features the koto. Dia plays the koto as a hobby.
The song features guitar riffs and an energetic beat. Mari composed the song and is a fan of industrial metal.
The choreography is full of Buddhist hand gestures. Hanamaru lives in a Buddhist temple.
The costumes are clearly designed with traditional Japanese influence. Ruby comes from an old fashioned Japanese aristocrat family.
Some of the lyrics are adapted from Yoshiko's notebook in Season 2 Episode 2.
In Season 2 Episode 6, Kanan is noticeably dirty when she appeared to check on Chika's progress for the dance move that she devised. She is likely practicing the same move in case Chika can't do it.
At the end of Over the Rainbow, we see what the two groups of µ's and Aqours truly represent. µ's is a legendary group that is only represented by the 9 idols. Aqours is a legacy group that started as a trio, was revived by another person, and eventually grew to 9 members including the original trio, and is passed down for anyone who loves school idols.
A light example: Yoshiko doesn't like mikans/oranges. So what was going through her mind when she suddenly had a mikan shoved into her mouth during the monorail ride (like all the others did) in Episode 3 of Season 2? Though it could be possible she joined the others in laughing it off.
A not-so-light example: Before Aqours performs MY Mai TONIGHT in the qualifiers, they get very little applause, even after their previous performances throughout the first season. What on earth caused their popularity to seemingly diminish like that?
Riko used to go to Otonokizaka, yet she's somehow completely oblivious to the very concept of school idols?
It is established, however, that μ's are winners of the second Love Live. And the journal, that Hanamaru and Ruby read in the fourth episode, was devoted to the 5th anniversary of the competition. So there is at least four years between the events of School Idol Project and Sunshine. Riko is in the second class in Sunshine, so she entered Otonokizaka right after Yukiho's and Arisa's graduation. She is also obsessed with playing piano, so she likely did not pay any attention to what other students were doing in their spare time.
Another reason is also revealed in Episode 12. Mentioned by an Otonokizaka student, the members of μ's decided to take away anything about them before their graduation.
Why is nobody questioning Yohane's fallen angel stuff...at Catholic School...likely filled with nuns/religious teachers that would be concerned about Yoshiko rambling about demons and Hell (well I presume, this is an anime after all)? I mean Yohane's delusions already run on the anime version of Catholicism and it's merely a backdrop for why there are no male students, but either Yohane is failing religious studies, or nuns are having heart attacks every day from her presence.
The nuns have probably seen other cases of chuunibyou and figure Yoshiko will grow out of it, especially given that she does seem to have some degree of awareness that it's all a fantasy (as opposed to someone like Rikka). The Catholic Church isn't as obsessive about fantasy occultism (like the Harry Potter series) as Evangelicals are; compared to, say, praying at a Shinto shrine (which most Uranohoshi students are probably doing anyway), engaging in a bit of occult fantasy play would be a relatively minor issue in Catholic thought, especially since it's something Yoshiko's unlikely to continue later in life.
As much as it was a wonderful moment for Aqours to make it to the School Open House after performing at the Love Live in Episode 3 of Season 2, they could have just asked Chika's sister to drive them there. Even if all nine idols couldn't fit in there they could have just asked someone they knew to drive the rest of Aqours there.
Regarding the English dub: When Mari is found to have fallen asleep in S2 episode 5, having put on fake glasses and stickers with blue eye designs, Ruby notes "the stickers are a nice touch", as if she never saw her use them before. Yet Mari had already pulled this sticker trick in Episode 10 of Season 1.
It's possible that though Ruby looked in Mari's general direction last time, she may not have had a good look at the sticker that's still on Mari's eyelid or the sticker that fell off. Ruby was worried over the just-fainted Dia, and got distracted by Chika panicking over Mito's Death Glare and begging them to sleep.
To be fair, it's just as possible that Ruby was complimenting the deviousness of Mari doing a two-part swerve this time, instead of just the stickers. How they all seemed to not notice both times that the stickers/glasses had the wrong eye colour - Mari's eyes being yellow and all - does seem a little suspect in retrospect...
No one seemed to remember or acknowledge Dia's birthday (January 1) in season 2's New Years episode.
The episode begins with Chika doing New Year calligraphy. It's likely her own version of kakizome, calligraphy that's traditionally done on the second day of January.
However, to confuse things, Yoshiko claimed she held a New Year's live stream the day before. It's likely that was for New Year's Eve, given she must have stayed up really late.
The dub has Chika's mom outright state it's New Year's Day. As such, maybe Chika felt like getting that calligraphy done early. So basically the girls still didn't acknowledge Dia's birthday.