The issue of Nayuta's sickness is directly addressed by cozmez' REVOLUTION track.

Kanata: What's the temperature?
Nayuta: Hmm... [sigh] 37.7 degrees.
Kanata: Knew it. You have a fever.
Kanata: Hardly. It's not a big deal. Anyway, who are you calling?
[sfx: phone tapping]
Kanata: We were supposed to make that guest appearance tomorrow. They've got other guests, so I'm gonna cancel.
Nayuta: It's not worth the effort. I just need to sleep it off and I'll be fine.
Kanata: Hm...
Nayuta: I'm just a bit tired. This is just what it's like with me.
Kanata: But... ... that doesn't mean you're operating at 100%, you know? You might go back to how you were before the experiment stuff. If that happens again...

Anniversary countdown art isn't a given; they posted countdown art from the original artists (less
Kuniharu Komiya) for the second anniversary, and year 3 posted the First Note special pages as a countdown and had art from the original artists (again, less Kuniharu Komiya) sequentially following the anniversary, but last year (year 4) the commemorative art was posted sequentially after the anniversary.

tl;dr: There's not a reason per se, it's just not a given that they do a preemptive countdown campaign. (Though as of ~45 minutes ago they have posted a teaser, but that's still not necessarily indicative that they're going to do a campaign before the anniv itself.)

So the literal line in question is:
一生檻の中で飼い殺した

The first part is pretty simple (一生檻の中で -> "My entire life, I'm going to be in a cage[...]") but the 飼い殺し is where I had to make some choices.

So 飼い殺し means, very literally, "to keep something while killing it"; it quite literally means, like, to keep a domestic animal alive past the point of its usefulness, or past the point that its quality of life is declining. It also metaphorically means to like, be keeping someone locked into a pointless job doing menial labor.
Basically, what's being conveyed is idea that he's basically just being left to waste away.

This is a very evocative image, but I think any way of putting it extremely directly in English doesn't have the same impact, especially considering the voice I tend to use for Kenta; he's pretty vulgar and he generally doesn't use five tactful words when two rude ones will do, so "left to waste away" or the like felt way too soft for him and for the way he's speaking in that line.
So that's why I chose to put it as "rotting", because that kind of has some of the same connotations-- of something that's dead or dying, and of just sitting around incapable of doing anything but waste away.

As far as I'm aware, there isn't any official statement as to any of them (though I hate saying this because I always feel like there's gonna end up being a magazine from 2021 that I don't have access to that explains it all, lol).

(This is slightly facetious/kind of a joke: I think a large part of this is probably the degree of freedom that the character designers have, since I'm 99% sure that all of [ex] Akan Yatsura's and GokuLuck's tattoos are just the result of Harada-sensei and lack-sensei respectively going "and I will splash a tattoo here, and here, and another one here, for funzies" and leaving the writers to figure it out.)

Answered once and re-answering because I hate adding extra context in replies that people might not read

First of all thank you! I passed out like a rock lmao

Second of all, and yes I am exactly this kind of pedant, the lines are:
"... 一番の財産は武雷管の修羅、辰宮 晴臣。お前だよ。> (EXTREMELY LITERAL) "His greatest asset was Buraikan's Shura, Shingu Haruomi. That's you."

So when the very next line is "命をかけて守ってくれた", I think it's safe to assume that since he's extremely explicitly describing Haruomi in sentence A, he's probably talking about Haruomi in sentence B. This is of course setting aside the fact that we already know that Haruomi risked his life to try and save Chisei, because Haruomi attempted the first metal kiss mind dive (see: VIBES drama pt.2-- though note that AFAIK this is actually the first time Buraikan have brought it up directly themselves!).
Then Chisei later says that he's the one who benefited from the inheritance more than Haruomi himself > he benefitted from Haruomi.

The reason there might be confusion is just because Japanese omits subjects a lot, so the literal sentence "命をかけて守ってくれた" LITERALLY just translates to "risked their life to protect [me, implied by the ~kureta]", with no explicit indication of who was doing it.

So if you assume he's still talking about Haruomi's father, that may be the source of the confusion; but the way I read it, the segue between "お前だ" and "命をかけて守ってくれた" basically reads as "you, [who] risked [your] life to protect [me]", especially with the later context of him saying that he's the one who benefited from the inheritance.

But I'm not making that assumption, again, because of later lines in the drama and the fact that we already know that Haruomi has done stupid things to try and save Chisei.

In terms of worldbuilding, there's no reason there wouldn't be female musicians doing phantom lives, if that's what you're asking.

This is extraneous rambling:

I know that some serieses do go out of their way to justify why the entire cast is male-only, or at least majority-male (obviously there's Hypmic's gendered worldbuilding as a comparison, since Paralive can never escape the comparison; but also things like Visual Prison, or even just the single-gender justifications for franchises set at schools), but Paradox Live doesn't.
The only reason that the entire cast of Paralive are men-and-Anne is, related to the last question I answered -- just because the series is aimed primarily at women who want a cast of ikemen, and so everyone who is participating in this one music competition just happens to be an ikemen (and Anne).

I think it's also good to remember that fact, just in general; remember that the story of Paralive is not really about huge world-changing events and winning doesn't confer, like, political power or whatever; it's just a music competition, and the phantom live music scene exists outside of it.

Without delving too deep into the weeds of it: marketing demographics are fake and made up.

Slightly more into the weeds:
I really don't want to shoot my mouth off about this, because (A) this is a very big subject that starts a lot of fights, and (B) I am a man and therefore my opinion is only worth so much in the conversation, and (C) I can only talk about a short paragraph in a single interview for this question.

But if you take Paralive in the context the other franchises owned by Gcrest? My takeaway from that interview isn't "it isn't a joseimuke franchise", it's "it's joseimuke but it's meant to appeal to other people too"... which probably means, in essence, they're not specifically targeting the women who are into otome games audience. There's no romance.

And to be clear: there is a profound problem in the association of "for women" with "features m/f romance". The idea that things for women, if they are enjoyed by non-women, are somehow suddenly not still for women at the end of the day, is pervasive and bad. But also oh my god I don't want to get into it.

If it walks like a duck, quacks like a duck, has waterproof feathers like a duck, paddles like a duck, and lays duck eggs, and gets featured regularly in magazines and stores that exclusively promote ducks? It's a duck, even if it's meant to appeal to people who aren't just hardcore duck enthusiasts.

(Prince of Tennis and Yowamushi Pedal are shonen on paper, but it's not men that made their stageplays full of flamboyant singing men successful.)