Taken data with using Internet on iphone?

When I'm out and the 4G is on my iphone to use internet but I don't go on internet just listening to music from my playlist. Is that still taken data

You won't be using data playing music from your playlist. However, if any of your apps update or use background activities, that WILL consume your data.

If you don't want to use data, turn it off. One click.

Updates of various sorts, turn it off when you arent using it

No, listening to music that is already on your phone does not use data.

If the music is on the phone already then no, otherwise it would be streaming so yes.