Can a school search your FaceBook account?

Unfortunately I think the answer to this is going to have to be "it depends".  A lot of law pertaining to privacy and Facebook is just emerging, different situations are being addressed by the courts in different states, and different results are being achieved.  If the computer is a "school" computer, and you are accessing the Internet via the school, and the computer is supposed to be used for school work, then I think an argument could be made that the computer and its contents are school property.  This happen often in businesses.  If my computer is owned by my company, and I am accessing the Internet via the company Internet provider, and I am only supposed to be using the Internet for work related business, then the contents of my computer belongs to the company, and there could be a very strong argument that a Facebook page created using that computer, and accessed on that computer, belongs to the company.  If however, you are using your own computer, and have your own internet provider, in a dorm room for example, I do not think the same could be applied.