Off the top of my head without more info I would say check your remote wire and make sure it is hooked up to something that only works when the car is running (i.e. turn signal fuse). If the remote wire is run into something that always has power your amp will stay on. As for the humming, it could be due to your amp being improperly grounded. Not sure on the stereo not turning off.
Oh, and welcome to FF