Speed Control Cable problems of the 2008 Chevrolet Malibu

On multiple occasions while driving, speed doesn't change outcome, door locks will continue to lock and unlock by themselves and car alarm will go off and will set itself while driving down the road. This is very distracting to the me, the driver and to the drivers around my car. Thus potentially causing a crash. Also, the brake lights will illuminate until you press the brake pedal then they go off. This is definitely backward! the doors will unlock, sometimes. However, you will have to guess which ones will unlock. Usually, the ones that unlock are the front-right passenger and back-left passenger. The reason the unlock is because they don't lock! no one can "duplicate the problem". The driver door and right-back door sometimes are unable to be opened. This requiring me to find a door that can be opened or that did unlock and climb through to the drivers seat. All of this while making sure my autistic son and daughter remain safe in a parking lot. This is very unsafe, as I park in a parking garage several times a week on a college campus. Unfortunately, neither key less remotes work either! most recently the shifter cable has broken. The care wouldn't budge. Chevy was notified, we were told to have it towed to the closest chevy dealer. Just to be charged a diagnostic fee, we told them the problem, and they decided not to cover it under the power train like we were told would happen. Then two weeks ago, the shifter cable broke again! this seems very odd. The entire time I have had this car when I press the accelerator pedal it feels like the car is running out of gas or like its having a hard time shifting. This has been reported from the beginning with no help. So, this is my last reach out for help. As I hear about all the carjackings, cars getting stolen and robbed, I just think my car is an open invitation! please help. Chevy wouldn't help us even under warranty.