彼女は日本の文化 and うまく馴染めるの phrase are noun
You don't seem to be parsing the sentence correctly.
彼女は［日本の文化にうまく馴染めるのか］、不安でならないようだ。
Here, 彼女 is the subject of 不安でならない, "She is really worried ~~".
「日本の文化にうまく馴染めるのか」 is an embedded clause, "whether or not she can adjust to Japanese culture well". (The implied subject is 彼女.)
The に marks the indirect object of 馴染める. 「日本の文化に馴染む」 means "adapt to Japanese culture".
So the sentence as a whole means "She seems to be really worried as to whether she can adjust to / get accustomed to Japanese culture well."