Sekai being the entity is very interesting. However, if she is the world itself, or was created by it, it raises many questions about the world itself - since it wasn't able to do anything up until that point. Also, Ami is possessed by something during Somnambula (which could be her hearing the world itself), and at that moment she was not able to hear Sekai - so I don't know about them being the same thing.
If she was, then it also raises the question of who created the two month skip, since there is some evidence that could be used to link it to the world itself (even though Yasu says that HE IS HERE - so I'm not certain about it simply not being HOPE). Also, the promise to bring Sekai back seemed to be given by HOPE way back, and she returns in his season after all.
I'm not certain Himawari was actively helping Sekai during her return, or just trying to keep his head from exploding in the process. Her presence as well as Noodle's also appeared during the night that Akira first recovered a flashback with Niki (there was a Sekai shadow in that though), so they could have been there more to the recovering of his memories being a part of their plan, rather than the Sekai return as an entity. BUT! that Himawari failed to protect Akira, ran away, and then immediately after Sekai hijacked the quiz is suspicious. It's almost like Himawari could have been plan A of this united front, and they fell back to plan B.
In relation to her killing Yumi, there is this, which takes place before the quiz. I don't know who that is, could just be one of the Mayas, or Yumi:
I'll keep playing and keeping a look as to evidence of who brought Sekai back, and her relation to the world itself/being an entity. Overall, I'm at least convinced that it was her that saved Akira during the 5th reset.
Side-note: There is also the Maya (or who that was in the first place) that leads him during the first reset to meet Saki, and I have no idea what's that about. And, more to the point of this discussion, Akira has been called Sekai by AmIOkay before. So that's also a thing I have to consider to some extent (although the simple explanation could just be that she was with him all along).
The World Itself not being able to do anything probably isn't accurate.
It may be the reason that the other School was swallowed, which led to the Nakayamas, Nodoka, Tsukiokas, and Otoha, all ending up in Sensei's class. The "sinkhole" could be interpreted as The World swallowing the School, and Yasu seemed wary of saying too much, otherwise it'd happen again, she also seems to think Red is Bad:
Ami being weird in her 'Somnambula' Event may just be Sensei blacking out. He was suggested to simply be dreaming. The eyes, USER1, and religious stuff seems to suggest HOPE was involved. The Nao eyes is probably Nao's involvement, though.
That floating person that appeared before 'Untitled' also seemed to appear behind Maya in The Scary Room:
And it seems like Sekai likes to float behind people:
It may just be Nao though, that's usually floating around. Of course, there's also that Maya face thing seemingly floating behind Sensei.
"A" may be for "Apple" as in Sekai's Happy Event song in the 'Something Everything Knows and Ignores' Happy Event. The S.E.K.A.I. Happy Event. That poem with Noodles and The Shapeshifter/Himawari, after Sensei remembered the night he kissed Niki, mentions an apple.
Nao mentioned "We" in the 'Mother's Milk' Happy Event with Sekai next to her:
So, they may be working together. That area they were in, may also be in the Tsukioka Manor:
As for why Yumi may have died, she could either have served her purpose (hasn't seemed important since), or she may have failed her own trial and simply suffered for it. The girls were going through trials while Sensei was:
Yumi may have also simply been "recyled" so that whatever intruded on the show could gain some power, quickly. Yasu seemed to imply that other forces can do stuff like that:
Or SeKaori just butchered Yumi to steal her place on the Roof, or something. Not really sure.
Is there anyone Sekai likes? Except Ami and Maya.
Sensei had children? He abused them?
Also, did Sekai also abuse her Husband? Was he a cuck, did he even know about it?
Sekai seems to have loved Sensei and Ami. The supernatural Sekai seems to like Sensei, Ami, Nodoka, and maybe Rin. Considering Sekai seemed to show up after Nao-chan was perved on by the plants, which end up dead, I'm assuming she likes Nao-chan. Possibly a few others.
Sensei seemed to more or less adopt Ami and Maya around 8 years ago. He also seemed to be somewhat of a pseudo father figure for Ayane since she was 11 (around 4 years ago), since hers seems to neglect her.
There's also his and Tsuneyo's kid (Noodles) which he definitely neglects.
Edit: Nozomu probably didn't know about it. He's implied to be more or less normal by Ami, and annoyed by Sensei flirting with Sekai. I somewhat doubt he'd approve of someone, especially his kid brother, fucking his wife.