Is a university student's use of a fake Facebook account to ask about the name of a young man she admires – without speaking in a provocative manner or revealing her identity – considered a forbidden act?

Your question about the name of the righteous young man and your prayer to Allah to make him your husband are not forbidden. It is permissible for a woman to offer herself in marriage to a righteous man, provided it is done within the proper Islamic guidelines and manners.