cruise control wont work if there are other problems detected by the bcm it's a built in safety feature, same for the auto start, and anything blocking the rear backup sensors ability to read the area they are designed to "see" will cause a problem. Also backing up faster than 5mph will shut the sensors off. If you installed something on the rear and it is not blocking the sensors then check the wiring harness to the sensors and see if you accidentally yanked one out or something in the process. the Buzzer sound is probably produced by the bcm and is not likely to be a separate device.