There's a fair bit in that lead up conversation you can ask about to start like his background, life, or interests. Just make sure you phrase stuff in the form of a question. "Do you know about x", "what do you think about x", "can you tell me about x", etc. There's nothing you need to ask about to proceed or anything that changes the story drastically. It's all background lore or easter egg stuff.
For spoilers sake if you wanted to find them yourself stop here. But if you wanted more direct things to ask...
So far I've found around 50 questions he'll respond to and apparently there's more than that.
Some good questions that I always like to ask if I'm doing a playthrough: "who is marked for death" is a good one, asking about the forest or what's in it have some unfortunate hints about future events, you can ask about his family, asking "What do you think of x" the only character he'll have a unique response to is Roswell. You can ask about the medals to find out just how many there are to find.
Finally, the only ones I've found that changes dialogue or effects the story so far.
"Do you like rabbits?"
"Can you tell me a story?"
It adds a small bit of dialogue to Tysons day 10 and for every route adds something extra to day 13.
And I always finish the interview off with "Can I thank you?"