By default moodle doesn't have such web service available to fetch quiz questions and answers,So you need create your own local plugin and implement web service there. ( * plugin are written using php scripting and i don't have much idea on php script )
Please find the below links which may be helpful for you.
http://docs.moodle.org/dev/Creating_a_web_service_and_a_web_service_function (Step by step explanation for creating local plugin)
Mohan Kumar B M