My daughter had to do this for school a few years ago. Both she and her great-grandmother enjoyed it!
You've had some excellent question suggestions, so I'll just add this: Be prepared for spin-off questions. For example, my grandmother told my daughters that she'd attended a one-room school house. My girls had no idea what that meant, so she explained . . . and it led to more discussion about how there was no cafeteria, no school bus, girls always wore dresses, etc. Those questions weren't on the list, but the answers were interesting, and they ended up in the paper that my daughter wrote.
She also told some things that I didn't know. For example, she explained why the road by our farm is curved. She said that the road was originally built so that kids could walk to school (which was actually quite close to our farm). She said that our pond used to overflow (which I didn't know because the road's been raised), and the road was built to skirt the typical flood pattern.
Someone else mentioned that they had relatives who wouldn't discuss the war. That wasn't an issue for my grandmother, although I know for a fact that she lost relatives in several wars. What she would not discuss was any love interests before my grandfather. She says that she was never even interested in a boy 'til she met him. I didn't say anything, but I doubt that was true. She met him when she went away to college; he was teaching high school in the same town.
Hint: My daughter had to write a paper about her relative's life, and instead of just writing it, my daughter did something creative: She wrote it in first person point of view as if she'd woken up in her great-grandmother's life. She wrote about feeding the animals, her father preparing a whole day in advance to take them to monthly church services, how she hoped they'd sing her favorite hymns and looking forward to seeing her cousins at church, and what they ate. It was a good paper.