How should a Muslim deal with his Christian colleague in studies, and is it permissible to initiate greeting him by saying, "How are you?"

It is obligatory to treat them with justice and fairness. It is permissible to engage in various types of transactions with them as necessitated by need. However, it is forbidden to appoint them to positions of authority or to take them as close advisors (بطانة) instead of believers, as explained in Fatwa no. 48060 regarding the ruling on not initiating greetings of Islam with them.