There is a way to do with the CC2015 (paragraph shading); depending on the scope of your project, and how often you need this function, it may well be worth your while to upgrade.
In CS6 it might work with auto-sizing frames with a fill color and text inset, one for each question and one for each answer, with the frames anchored into a larger text flow. I have not tried this, though.
I think there were also some scripts floating around that would add paragraph rules above and below to make the shading, and could calculate the size based on the number of lines. You'd have to google for them, I'm afraid, and it would not be automatic, nor would it update if there are edits unless you run the script again. If you do a lot of this, Ghent upgrade is almost certainly worth it.
Thanks for the replies. I wish I had CC but unfortunately I'm stuck working with CS6 here at work. Peter I'm not sure what you mean by your first paragraph?
Scripts wouldn't work as I need it to be automatic.
Thanks again for the replies