It is possible to study Arabic and other subjects in the West Bank. Specifically at Birzeit University near Ramallah.
If you are interested in learning about the social, political and cultural aspects of Palestinian life, there are several programs and organizations offering courses, workshops or learning tours, such as: The All Nations Cafe (http://www.allnationscafe.org) in the Bethlehem - Jerusalem area, or Green Olive Tours (http://www.toursinenglish.com/), that offers organised informative and political tours throughout the whole of the West Bank.