Is it possible for a psychopath to be a Christian? How can I help support such a person's faith development?
Yes, most certainly. Christ calls all to follow him, especially those who are troubled: "Come unto me all you who labor and are heavy burdened, and I will give you rest" (Matt. 11:28-29). It is true that psychopathologies in various degrees limit the human freedom of those who suffer from them, so the person who suffers in this way will not be held to the same standard as someone who does not suffer in this way. There will be certain thoughts and actions over which the person has little control.
What the psychopatically troubled person needs to do is to be willing to follow Christ by seeking healing. He or she can show love for Jesus by wanting to see the world and others in a peaceful and loving way, and seeking through therapy and even medication to become more whole. This person needs to have around him fellow Christians who are charitable, who are patient with his condition, and yet are willing to challenge him to do what he is able to do to get better, or at least not to get worse. Offering to pray with the person, for example the rosary and the litany of Our Lady. Some time of quiet adoration of the Blessed Sacrament is a necessary means to finding healing and protection from the troubles that accompany mental illness.
Remember that some great saints—for example St. Thérèse of Lisieux—suffered from mental illnesses and were healed of them.