What is the ruling on communicating via Facebook with a colleague with the intention of proposing marriage, while limiting conversation to general, academic, and religious matters, and without exchanging words of love and passion, and without meetings outside the school setting?

It is not permissible for young men and women to get to know each other and converse via the internet or any other means, even if it is for the purpose of marriage, because it is a door to temptation (fitna) and a pretext for corruption. If the young man is sincere in his desire, let him propose to you. If he is not currently able to marry, then you must cut off communication with him. Do not be deceived by the absence of expressions of love and flirtation in the conversation, as that may be a lure from Satan.