What does 坏坏的 mean in "坏坏的问道"?
Yes, 坏 is usually bad/broken, and 问 is ask. However, if boys want to play tricks on girls, for example, boys ask the girls 'have you ever heard some strange noises from your parents' room?' 

In this scenario, we can say the boy 坏坏地问道：“ have you ever heard some strange noises from your parents' room？”