If you're pads are new and squeaking its because the shiM behind the pad squeaks when pressed by the caliper against the rotor. It makes it sound as if need a brake job even though the brakes are brand new. To fix it you go to autozone or advance autoparts and pick up a tiny pack of "stop squeal" or brake squeal stop, they carry it at the registers. Take the wheels off, calipers off, pads off and apply this stop squeal gel/goo to the back of the pad. Then put everything back and your noise should be gone.
I don't see how having the engine running affects the bleeding of the brakes? This makes no sense to me.. Just make sure to pump the brake pedal ~30 times before doing the brakes with the car off to pacify the ABS system