People make me, save me, change me, raise me. What am I?

You see me when a storm comes in, and when I leave, my name describes how quickly I go. I always come with an echo, although the echo can be near or far. One can tear everything apart but I am also used to hold things together. What am I?

When I begin with 'P', a wrinkly one you've got, You have me, but hope that it's never ever shot, I can also dispense liquid, warm to the touch, But to be honest, most people don't think of me that much.

I can be a puppet for your kids, a toy for man's best friend, On cold winter days, your feet I'll attend.

Piercing in tone, More Callas than Bocelli, Your throat holds your song, Mine seethes in my belly