Q: When listening to a playlist offline with the Music App does it use data?

It will only use data when playing a song that is not downloaded directly to your library. You can disable data use to stream music through your settings and just make sure what ever it is you want to listen to is downloaded over your wi fi, as to not incur data overage charges with your provider like i have to because i was unaware my transferred music from iTunes to my phone no longer existed and was streaming my own music for an entire month! this new music app is horrible!

No it will not. It will only get data once you're playing those musics/songs that are are not saved or downloaded on your iPhone, I suggest you to use iTunes instead.