* Noise cancelling earphones really do cancel the noise before you hear it - when they're fast enough.*
No. They can only start cancel ing it after they build the predictive model of it, and only if the model is accurate. Basically this only works for repetitive regular types of noise (e.g. engine hum).
When they work you feel like you're at a quiet room, weirdly hearing only the high-frequency sounds.
But yes, you can listen to music at a much lower volume, Safely.