"Nani" is essentially "what" in Japanese, and it isn't that strange that Nanase would say it in a reactionary fashion. Japanese is the language she speaks around the house with her family, after all. Still, she spends the rest of her time with people who primarily speak English, and it's potentially confusing for readers, so she hasn't said it much in recent years.
And I guess she's still referring to her fairy doll as a "fairy avatar"! Sounds fancy, sure, but I think I like "fairy doll" better. Also, I'm pretty sure Nanase can't bend all four elements*.
* Why yes, I did finally get around to watching The Last Airbender
Commentary added for December 31, 2014