When I press a button on a different scene, Can I make it change something on a different scene?

For example, Lets say I have a settings scene and there is a button to turn the music off on a different scene. Is that possible? If so, how do I do it?

Yes, although there are a few dozen ways to do it, my recommendation would be have your button update a Global Variable, rather than a scene variable.

Then in your other scene, have it look at that global variable for whether it should have music play or not.