So, here's the promised post about the Chrysos Heirs' speech patterns in Japanese! Be aware that this is all based on what we've seen throughout 3.0 alone, so we might make new discoveries next patch! Here we go:
Her first person pronoun is 私. Normally, it's read as watashi, but Aglaea uses it as watakushi instead, a more noble and feminine form. Her second pronoun is the polite and standard 貴方 (anata), and she usually uses the gendered 彼/kare (he/him) or 彼女/kanojo (she/her) for third person. That last thing might not sound special, but Japanese has a myriad of ways of addressing people without referring to gender, so it's a sign she goes the extra mile to sound more formal.
Talking more about her speech patterns, she's very polite and formal in a distinctively feminine way. There is a form of Japanese known as 敬語 (keigo), which is pretty much "Polite Japanese" and the form a non-native speaker would learn first because it's what you'd use the most. The interesting thing is that Aglaea always speak in keigo, regardless of who the other person is; she never defers to a more informal speech.
In fact, the only times her speech seems to change is when she adopts an outright reverent tone. I talked a little about this before, but Aglaea addresses the Tribios by 我が師 (waga shi). This word choice by her is particularly interesting for two reasons:
1.) The use of 我が (waga), an ultra reverent way of saying "my/mine". It makes use of the pronoun 我 (ware), which is really archaic and not part of modern conversation except for a few expressions such as 我ながら (if I say so myself).
2.) The use of 師 (shi) for "teacher". Usually you'd see the common 先生 (sensei) around, or maybe even 師匠 (shishou), which carries the extra connotation of "master", but Aglaea uses only the first kanji of 師匠. That makes the whole thing sound beyond reverent.
Aglaea also addresses everyone by name properly, even the ones who usually go by nicknames like Mydei.
The three speak the same way, the only difference is each one says things according to their personalities.
Their pronouns would be あたし (atashi), a feminine and more informal form of watashi, but as they refer to themselves in plural, it becomes あたしたち (atashi-tachi). They don't actually refer to other people in second person or third person pronouns that much, preferring to use names (or nicknames) instead. It would sound weird in English, but it's a perfectly normal way of addressing people in Japanese, even more so if you're a kid.
Talking about kids, as you'd expect, the Tribios speak exactly how a very excitable Japanese little girl would. The nicknames are a part of it, but it also doubles to highlight their importance in Okhema (you're allowed to be a little more informal if you "rank higher" than the other person in Japanese). The only time they break away from their pattern is when they're reciting the chants to borrow the power of the Three Titans of Fate. There, they adopt the reverent tone you see with Aglaea.
As an addendum, the suffix ちゃん (-chan) the Tribios attach to nicknames is supposed to be used for people younger/less experienced than you or someone you find cute, especially kids, but it's generally more accepted for girls. With a boy, it's more common to use くん (-kun), but the Tribios use -chan regardless of gender.
In short, the Tribios are kids who treat everyone else like kids.
His first person pronoun is the masculine 僕 (boku). It's not very formal but it's still on the polite side, and it's commonly used by young men. His second person pronoun is 君 (kimi), which usually denotes familiarity, but he uses it regularly regardless of who he talks to. As for third person, he uses kare and kanojo depending on gender, but also can use アイツ/aitsu (that person) if he wants to be less informal.
In general, he speaks like a cheerful young man of this time would, but since he's Amphorean, it also gets mixed with the prose-filled speech you can see in pretty much all the characters. You can see him attach a more modern suffix to words like っぽい/-ppoi (-ish) and then address the Trailblazer by 我が友/waga tomo (my friend) not much later.
On the topic of 我が友, you might have realized this already but it works on the same principle as Aglaea's 我が師: using the reverent pronoun 我 followed by a single kanji, this time 友 (which is the first kanji of 友達/tomodachi). It kind of speaks volumes about Phainon's appreciation for the Trailblazer.
Interestingly enough, he addresses the Tribios by sensei and Castorice with the suffix さん (-san), but he simply calls Aglaea by name alone.
Just like Aglaea, her first and second person pronouns are watakushi and anata, and she uses gendered pronouns for third person. The only difference is sometimes she addresses people by 方 (kata), which is remarkably polite of her.
Yes, she's polite. Very polite. No, I kid you not, she's the most polite character I've seen in years. I talked a little about keigo with Aglaea, but it seems Castorice speaks in 尊敬語 (sonkeigo) specifically, which is just Japanese Customer Service Voice™ . As a result, her sentences are at the very least twice as long as anyone else's would. The only time she breaks character is while translating Oronyx's words (which was hilarious because Oronyx was being ultra condescending the whole time).
Castorice makes ample use of honorifics. In fact, I can't remember a single time she didn't address someone by -san or 様 (-sama). She's incredibly consistent in that regard.
First person pronoun is 俺 (ore): masculine and rude as hell. Second person is お前 (omae), which is also rude as hell. Third person is コイツ/koitsu (this person) and アイツ/aitsu (that person), which are gender-neutral and incredibly casual. As you can see, he doesn't give a fuck about consideration.
Despite the pronouns, Mydei can actually be formal and even flowery in his speech, as expected of an Amphorean. He's very much not polite at all, though. His speech is also very masculine and gives the overall vibe of a very arrogant royal (almost like a certain golden king of a certain franchise, huh). Sometimes he gets a little... Indulgent, I'd say, and that's when he's on something like a good mood.
He did the 我が thing at least once too; in his case, it was with Chrysos Leo, who he called 我が師匠/waga shishou (my master). Note that he used 師匠 normally, unlike Aglaea who only used 師.
He rarely addresses people by name. Usually, it's either titles (like with the Tribios and Phainon), or a rude-ass "you".
And that's all for now! Corrections and additions are welcomed, as I am not a leading expert in Japanese or anything like that.