Is it permissible to study at a mixed-gender university in America while adhering to Islamic dress and trying to avoid men, and does the hadith "Seek knowledge even if it is in China" include women?

A girl's study in mixed and corrupt societies is impermissible. The Hadith "Seek knowledge even if it is in China" is fabricated (mawdu'), and the authentic Hadith is "Seeking knowledge is an obligation upon every Muslim." What is meant by it is the Sharia knowledge, for which a Muslim is not excused for being ignorant of.