The sudden appearance of Alina was indeed pretty jarring. Like she appeared in middle of very important scene and we're just supposed to assume they know each other and are close friends or something. Also I'm not entirely clear which part is the truth and which is fiction, because it's kinda implied the jumping from rooftop and meeting Touka and Nemu was what lead Alina to be admitted to hospital instead of Ui and that's how they bonded. I didn't watch her episode story yet, but I guess it might help making a bit more sense unless the story that is told there is the fake one.
Alina's side story explains it: Touka and Nemu are the ones who found Alina after she jumped; Alina had no real interactions with Ui, but was aware she was their friend.
I understand that as Kyuubey is emotionless, it allows him to collect impurities without being affected by it whatsoever, while human would feel all the despair present in it, leading to them experiencing it and in turn starting to product their own impurities. What I don't understand is why as soon as Ui gained the power, she started collecting them unconsciously. Other Magius clearly had 100% control over their power and didn't use it unwillingly, so I don't understand why Ui is the only exception.
Except their plan more-or-less relied on Ui's being a passive power. Also, they explicitly stated they wanted Kyubey's powers, one of which was passively vacuuming up the despair energy needed to counter entropy.
On that topic, I don't understand why she started collecting them asap, but also then why she didn't start collecting them as soon as she woke up and instead now seems to be in full control?
One reason: Alina's barrier is still up, so there aren't anywhere near as many impurieties to deal with as when she first transformed, especially with Eve locking so many of them away.
I liked the touch with origins of small Kyuubey and I see one of theories I heard turned out to be semi-true with him not exactly being Ui, but rather possessing her soul. On that topic, next inconsistency is, that why Iroha was the only one who regained her memories after touching small Kyuubey, but not Magius. Would think that would solve all the problems.
The reason for using the small Kyubey was to cut off Ui completely from her fate. Since Nemu and Touka were a direct part of that fate, it stands to reason there would be a stronger barrier between them and the wall they themselves constructed.
So, what was up with that Ui showing up before Homura telling her to come to Kamihama?
I always saw this as an abandoned plot thread: they promised Madoka would go looking for Homura, so they had to set up a situation where that'd happen.
From other stuff, what was up with Mifuyu supposedly losing her power? It was mentioned multiple times through out the story, so I thought it'll be significant, but turns out when it mattered the most (defeating Fendt Hope) it didn't really matter?
It actually did matter plenty, but just not in that context. It was very much Mifuyu's motivation for a lot of what she did.