There was no fixing done in this. Diana just calls Natori (which is her actual name) Natalie because she mistakes it for it. Natori being a Japanese name is probably very foreign sounding to the European coded Diana so she instead calls Natori as Natalie because it's the closest equivalent...
Completely average. I'd say it was a good entry point to the story since it's the anime that lead me to binge read the manga but comparing the manga adaptation to the anime, the manga is clearly superior. There's just a lot more love and care put into the manga whereas the anime is a pretty...
Now Zagan's off hand comment about mana transfer is a smoking chekhov's gun. I'm gonna bet Barbatos will need some sort of mana infusion to recover and Chastille's gonna provide it.