There's an idea that I've been playing with, but I'm not sure yet if it stands up to any scrutiny. Is it possible that none of the Sekais we've seen (outside of memories/happy events) are real, and it's all just Pareidolia putting on a human mask?
It somewhat depends. Restored Sekai has been shown to possess Sensei, the black Angels possessed Makoto and Futaba, and this Sekai seemed able to physically touch and lift things as if it's simply invisible:
Presumably, these Rabbits are "real" and have weight, etc, so if Sekai can actually move things, then it might as well be "real". Yasu also seemed to hear her speak.
A Sekai has also seemed to murder the Plants, and possibly Yumi. Maybe even Todd and Makoto's father. Of course, the plants may have simply been within Sensei's mind, so it's hard to count that as "real" even if Nao-chan traveled there with him.
Presumably, the Shapeshifter/Himawari as a Narrator even seemed scared of this Sekai:
She's also seemed scared of what Long Maya could do, implying that Long Maya's actions can have actual effects on her:
Through the Shapeshifter, one could assume the Mayas and Restored Sekai are about as "real" as she is.
And we've been led to believe the Shapeshifter can affect physical things since she's sold those scarves, watermelon, wanted a cafeteria, and notably touched Ayane:
And gave her that daisy pin, etc. So, she's likely "real" in some shape or form.
Besides the Restored Sekai, the one at her grave seemed to genuinely love Ami as others have pointed out, and implied she had things to do:
Whether this one is a hallucination on Sensei's part or not, isn't clear.
Pareidolia on the other hand doesn't seem to care much for Ami, and doesn't seem to be able to do much more than mess with the minds of people, albeit, a Narrator did seem wary of it, and it possibly can teleport people?
Kaori and Sensei seem to be able to go wherever they want. Although, that might be less Pareidolia and more just their own abilities. Slipping through dimensions or something. The Shapeshifter implied one had to slip through dimensions to get back to Kumon-mi once:
Which would suggest that She, Sensei, and Nodoka can do that kind of stuff (since they can leave and reenter). I assume that's how Kaori gets places, and probably how Sensei has, without understanding how.
Still, Pareidolia does seem to like tormenting Sensei, and has called him "aki-kun" before:
Not to mention seems to be a fan of Sekai's:
So, seeing as how it seems to copy others, I can definitely see it copying or using Sekai to accomplish it's goals. Presumably the White Dress Sekai is it's, and Sekai seemed to invite Sensei to bed after what happened to Karin in her Chapter 4 'Paranoid' Event. This could imply that Pareidolia tried using Sekai to calm him down afterwards.
