Is it safe to leave an iPhone 5S on charge all night?

And also, is it safe to listen to music while it's charging as well? I can't sleep without music and my battery seriously needs charged before school tomorrow.

Yes it's perfectly safe, most people leave it charging over night.

Yes, not only have I always done this with my iphone 5S, but I did for several years with my previous iphone and never had an issue. You can't overcharge an iphone.