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.
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.