Does listening to music on your phone use data?
the answer to this question is multifaceted and it is yes and no. :) If you are streaming music via spotify, youtube, pandora etc. yes it does use data. Unless you have one of the cell providers where they do not count data used with certain apps.If you are playing music that is stored on your phone it does not use data.
Does listening to music that you download from iTunes use data?
If you mean music you download on your iPhone, and you download said music over a cellular network, then yes, it uses data.It does not use data to download one a WiFi network, or if you play it once it is downloaded.Keep in mind that if you are streaming music, it is being sent to your phone from the server from which it is being streamed, and will use up your cellular data unless you are on a WiFi network.
Does using phone while charging bad for the battery?
I do it all the time, I will be using my phone, have it get down to like 12%, and then I'd start using it while it's on the charger. It charges up real fast and even to 100% just fine, and the battery has been draining slowly for years. Yes, I said years. It should be fine.