Negative thoughts, sleep deprived.

Hi.. first of all you and your family need to stay calm and change the family's atmosphere. In other words try to behave normally in front of your father because if you all get anxious it may increase his stress levels even further. Help him in making a activity schedule and encourage him to follow it. If you are constantly talking about dealing  with negative thoughts and constantly trying to teach him how to overcome them you need to stop, instead just try to keep him distracted I am not saying that don't care for him but Do not over sympathise with him. Don't worry there are treatments available and he will be fine. I also feel he needs to vent out so Psychotherapy sessions from a Clinical Psychologist will definitely help him. From your description of his symptoms I feel he may even require to consult a Psychiatrist to prescribe some medicines. Just follow this and he will be fine.

I appreciate your concern and observations about your father. Probably,  he his under some problems,  which he is not able to share with you for his own reasons.

Fix an appointment with a psychologist and help him to get a clarity to come out of this depression.