No, it doesn't. It only has a built in microphone.
To record audio from a lapel in the field there are two main options... record directly into your phone or to a audio capture device, such as the zoom H4N.
I believe it will. However, the main point of this camera is its powerful zoom. Do you need such zoom for indoor dancing? I believe that the camera is suitable for such application. How far from the subject you are?