What are a cancer patient's emotional and social needs?

This is like all of. The crucial questions of life: love & fear. You can get all of the fear factors of what will the cancer do, and what will the treatment be like leading to how many days are left in all senses of that. We all fundamentally are here to love and be loved. Cancer does not change people, it magnifies their virtues and vices. Some need to make peace, others prepare for another day.
Varies among people. As with any other circumstance or life event, different people have different needs. Social workers who deal with cancer patients may be able to provide guidance.
Dramatic variability. There is no 1 easy answer to this question. Everyone is different. Try to be supportive and helpful. Asking questions about needs and wants might also be helpful.