Clarice is a real name, actually. It's the Germanic spelling (which extends to English spelling, somehow) of the Latin Clarus, meaning "Bright" or "Famous," and the Greek Clarissa meaning "Brilliant."
Feifei's Taiwanese? Learn something new every day... Doesn't make it make anymore sense, though.
I will say that Anastasia has stolen whatever part of my heart Yui didn't already have. However, I think she's only half-Russian, since her hometown is listed as "Hokkaido." But Not Too Foreign is a pretty common trope in Japanese media, for whatever reason, so it wouldn't be too out-of-place for iDOLM@STER. (Remember how Takane was originally one-fourth German or something?)