The word fushigi appears plentiful in Aria. I'm watching Tamayura, by the same director as Aria, and the word fushigi is in there a bunch too. He seems to like that word, and now I do as well.

Maybe. The encounter with the big cat was definitely fushigi. That's first thing that came to my mind, speaking of this sentence. Though, there were plenty of moments, when Akari could say that.

She also really likes the word "deai", and talks many times about loving to meet people if I can remember that correctly. Recently I re-watched episode 10 of The Natural where Aika and Alice follow Akari who meets the puppet master. Akari describes it as an "sutekina deai". Aika calls Akari "makka fushigina yatsu" which I thought was funny. It's one of my favorite episodes.