Puella Magi Oriko Magica/Fridge

Fridge Brilliance

 * It's almost certain that if Madoka would have been left alive, she would have became a magical girl so that at the very least Kazuko-sensei would be brought back to life. If Madoka's willing to bring a random cat back to life, she'd definitely jump at the chance to bring her beloved teacher back to life too, and Kyubey would more than certainly press that button.
 * Not really, someone's relationship with their pet is usally much closer than their relationship with their teacher.
 * It wasn't her pet, it was a random cat.
 * It's also been stated that Kyubey can't bring people back from the dead, although Madoka's potential might have been strong enough to override this by that point.
 * There's perfectly good reasons why Oriko doesn't get involved in the timelines we see: In three of them, Madoka dies before she gets a chance, twice because she dies to Walpurgis, once because Homura mercy-kills her. With the exception of Timeline 3, it's obvious to assume that Homura put a stop to Oriko before she could even get involved. But Timeline 3 was also the only one where all of the main cast was working together, so they may have stopped her before she had a chance to really enter the plot.
 * Keep in mind that Homura was no longer her older persona. So somewhere between the 3rd and 4th line. Also has unfortunate implications in that she might have offed them herself to protect Madoka...
 * We already know that post-timeline 3, one of the very first things that Homura does is kill Kyubey to prevent him from contracting Madoka when the black cat is hit by a car, which happens in the week between Homura being released from the hospital and the day she starts school. It's entirely possible, for the purposes of making this story fit into the anime, that she has also added "Assassinate Oriko" to her to-do list, and she just kills the other girl out of hand every time she repeats the month. Prior to timeline 3, it's easy to just say that Madoka doesn't have the crazy levels of magical potential that she does later on, and thus doesn't trigger Oriko's visions.
 * This would also show the line from which Post-Moemura no longer is able to communicate with Madoka emotionally. In Oriko; we see her Glasses Come Off self; but she's still able to rekindle her friendship with Madoka and not alienate Sayaka. Having to kill Oriko/Kirika makes her no longer innocent enough to connect.
 * The reason why she might not be able to connect to Madoka could also be because Madoka usually retains the last few moments of her life in the previous timeline, and in her last moments, Homura was acting like a jerkass who only cares for Madoka and not for everyone else.
 * The third drama CD for Madoka Magica reveals that  was a bit like Yuma - she was even a Third Person Person.

Fridge Horror

 * In the picture of the Witches who appeared in the story alongside their magical girl forms, Cecil and Stacy are no older than Yuma. This means that they became Witches as little girls.
 * Yuma's introduction has her being rescued from a witch by Kyoko. Now suppose that didnt happen in other timelines(either Kyoko never arrived or came too late), then Yuma would've died along with her parents. It might explain why Oriko doesnt become involved in other timelines. Without Yuma to use as a Red Herring against Kyubey, she doesnt or cant form a plan to kill Madoka (Yuma was in the 2nd vision she saw immediately following Gretchen Kriemheld).
 * Except, Yuma was saved as a direct consequence of Oriko seeing her in a vision. Because Oriko did see her, and therefore started the killing magical girls plan, Kyoko took over the unclaimed territory (which had belonged to some of the dead magical girls) that Yuma was attacked in. Because of that, she was there to save her life.