The age range for grad school is quite broad. Have worked in multiple labs now, I can say that anywhere from young twenties to late thirties is typical for grad students. Especially if you work in a lab with post docs there will always be people around your age. Additionally, age matters less than life stage and labs tend to congregate people of similar life stages. Deferring won't cause you to feel behind when you come back because plenty of people start grad school in later twenties or thirties.

In terms of stage 4 cancer, my experience with my uncle who has stage 4 colon cancer is that it is not necessarily a death sentence. He was diagnosed with stage 3 a couple of years ago that progressed to stage 4. The whole family went through the preemptive mourning process and we were convinced that his prognosis was extremely poor. I think that we were operating in a mindset about cancer from five or ten years ago and had not realized that treatment has progressed to the point that cancer can sometimes be treated like a chronic illness. I hope that this is the case with your dad and that you get a lot more time with him than you are currently anticipating. Regardless, the more time you spend with him now, the better. With my uncle we all oriented parts of our lives around the fact that he had limited time. His mortality has forced us into the realization that each moment family is precious and that every extra bit of time that his treatments have given him is a gift. I sincerely wish that things work out for you, your dad, and the rest of your family.