The squeal is the vibration between your disks and pads and is usually caused by a build-up of brake pad dust on the brake calipers, or from pad or disk wear. It is often indicative of a stuck pad in the caliper. Sometimes a blast of air into the calipers with an air hose will clean the dust out. If the pads are good and the disks are not worn, scored or warped, then removing the pads, cleaning around the calipers and replacing the pads with a small amount of copper grease on the sides and back of the pads will stop any squealing. Obviously great care should be taken to apply the copper grease only to the rear and sides of the pad and not to get any on the front of the pad or the disk.
Some varieties of brake pads are more prone to squealing and softer pads are less liable to squeal. Excessive squealing can cause the brake disks to glaze and then they'd need to be re-surfaced. So this issue is best sorted out early.
Perhaps the "death star" sound is the same cause, but at a lower frequency as the car comes to a halt and the wheels stop. The sound may then become more of a low groaning noise.
Please ensure your brakes work perfectly and if there is any doubt get them checked by a competent mechanic.