In an interview with my father about his life, what sub-headings should I use to organize the questions? Such as childhood? career?, personal life?
I would say that the subheadings that you use should be based to some extent on what issues you really want to address (what you are especially interested in) as well as on what has happened in your father's life.
I would agree that childhood and career and personal life are good ones. But are there other things? Did he move from place to place, for example? If so, you could ask about various places he lived. Did he serve in the military? Did he face any significant decisions that he had to make? Any particular hardships?
All of these are things that you might ask about. When I did a similar thing with my father, these were some of the major categories I used (except for the military) because I knew my father had had many of these things in his life.
So, I think you should tailor your questions to his life and to your interests.