I'd ask questions about the story itself. As an author readers have gone very in depth with questions about my characters and we speak about the story as if everything is real. They have at times given a comparative insight that I didn't notice. I like that readers are interested in the story as much as the process.
--- How an author got started, when they started writing, when they were published, how long it took them to write the novel, how they defeat writers block, most of that information can be found on their websites.
--- Ask if they outline when they write or if they just 'wing' it as they go along. Find out if they listen to music as they write. What types of things are in their office as they work. Do they have a character or story they particularly love. Are character names important to them. Do the novels they write end up with the titles they originally started out with.