I'd ask where the inspiration comes from. Does it come visually or aurally? Do they get snatches of lyrics first or little bits of melody first?

If they are asked to write a song about $topic, is it hard to find the inspiration - where do they start with that?

What do they do before they perform? Do they listen to recordings of what they're about to do? Have a playlist (like a lot of athletes have a playlist to psyche themselves up)? Do they like complete silence?

For trivial stuff: favourite song when happy/sad/angry. Favourite song to sing, to play to perform.

Hope that helps, or gives you some ideas!