Praise be to Allah.
With regard to girls studying in these mixed societies and in this corrupt environment, please see the answer to Question # 5384.
With regard to the hadeeth mentioned, “Seek knowledge even if you have to go as far as China, for seeking knowledge is a duty on every Muslim,” Shaykh al-Albaani said in Da’eef al-Jaami’: “(It is) fabricated.” (no. 906).
The proven hadeeth is that which was narrated by Ibn Maajah from the hadeeth of Anas ibn Maalik, who said: “The Messenger of Allaah (peace and blessings of Allaah be upon him) said: ‘Seeking knowledge is obligatory upon every Muslim.’” (220. Classed as saheeh by al-Albaani in Saheeh Sunan Ibn Maajah. What is meant by knowledge here is knowledge of sharee’ah (Islamic knowledge). Al-Thawri said: “It is the knowledge for which no person has any excuse for not knowing.” And Allaah knows best.