What you are referring to is a flashback scene regarding a tournament that the main characters are now training for. It shows that Yue and Ku Fei competed as a duo in a previous running of the tournament, some time after Negima but, by their appearances, long before UQ Holder.
Evangeline is alive, and serves as one of the driving foci of UQ Holder. She’s not quite a main character, but she is a major character that motivates the primary main character. Fate Averruncus is alive, and currently serves as the primary main character’s antagonistic rival.
He does not appear to be an active villain; the main character just wants to be stronger than him.
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The cat girl you reference may be related to Koyomi, as suggested by Torisuda. Their personalities don’t seem to match, so she may be a descendant of Koyomi, or simply another member of the same race of demi-humans. Maybe Fate just likes cat girls, or it’s a bit of nostalgia, or it’s a coincidence, or any number of things. She hasn’t been a significant enough character to be sure.
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Also alive is Mana Tatsumiyathe half-demon gun user. She is the one that introduces the main characters to the aforementioned tournament.
Since Mana does not appear to have aged significantly, one assumes that other half and full demon characters, such as Zazie, are also alive, but they have not appeared or been specifically referenced. Negi himself is confirmed as “alive”. This state is what drove Fate into an initial villain role, but eventually they held him off long enough for the protagonists to learn his aims and to negotiate a cease fire of sorts.
Since Fate’s goal was not especially time sensitive, he did not actually need to press it as strongly as he could have. No other characters from Negima! We can conjecture a couple more, at least, in addition to demons such as Zazie. Many fans think that UQ Holder occurs during the timeline where Asuna had not come back: Asuna’s lineage was also stated to be an exceptionally long-lived one; she was already quite old, technically speaking, when Nagi encountered her.
When Asuna did finally finish her task, she found out that her best friend Ayaka had lived well pastin hopes of meeting Asuna again. Since UQ Holder is set approximately 80 years after the end of Negima, it is plausible that she is alive. And we can get a little bit meta: UQ Holder is a society of immortals, several of which we know are well over one hundred years old.