Lutecia's transformation into a Genki Girl makes sense when you consider that among the Numbers Cyborgs, she spends the most time with Sein and Wendi, and this continues when she's in the rehabilitation center. Presumably, their cheery personalities gradually rubbed off on her, since she seems to like that part of them. That and she has her mom back.
Corona mentioned that when the Yagami family participated in their training match/mock battle, they completely dominated the field. Another case of Informed Ability right? That is until you remember what kind of mage Hayate is, and the kind of magic she's capable of. And with the best possible protectors, all she has to do is wait until her spell is complete, tell her knights to get the hell out of the blast zone (or have Shamal teleport them out), and nuke the field, effectively eliminating all opposition in one swipe.
Before their match, Sieglinde Jeremiah stated she had a good idea of Einhart's fighting style despite the matches ending in only one hit. She most likely got most of the things she needed from Einhart's match with Corona. The match itself took two rounds, which allowed Sieg to notice most of Einhart's strengths and possibly her weaknesses.
Vivid in the clone of a king famous for being the strongest. But while no pushover, she isn't on Olive's level. Why? Partly because of different upbringing and partly because while Olive had a Relic Core (inherited from her mother) in her body her whole life, Vivio's was destroyed by Nanoha in the Cradle at the End of the StrikerS season.
Rio has several Chinese elements and Micaiah has Japanese, but isn't Earth an insignificant little blue planet? Well, Subaru stated way back in StrikerS that her father's ancestors were from Unadministrated planet #97, so it won't be too surprising if others of Japanese or Chinese descent were living in modern Mid-Childa.
Sieglinde's Kansai-ben dialect. She isn't from Earth, but Mid-Childa, but why does she speak Kansai-ben? Do people on Mid-Childa actually speak Japanese? The main language seems to be English as seen on several on-screen textes, and the Japanese words on Harry's coat are referred as a "foreign language".
Presumably it's a Translation Convention. She's speaking with the Mid-Childan equivalent of a Kansai accent and it gets translated as Kansai-ben (kind of how Kansai-ben is often turn into a Brooklyn accent in dubs). Also, this user thinks it's probably unlikely that Mid-Childa actually uses English as their main language (that being Earth creation) and again it's a translation.