This is caused by a construction flaw during construction of the tire. If it is a fairly new tire it will be replaced by the manufacture.
No, it is more likely to shift if the tire is rotated in the opposite direction. No, damage from a hard impact or a puncture will cause a slipped belt.
Yes, a "slipped belt" can cause a tire to squeak. A slipped belt is when the belt area of the tire separates from the radial plies of the tire and there is a noise as the two parts rub across each other. If a tire squeaks because of a slipped belt, do not drive at high speed and replace the tire as quickly as possible. A slipped belt will eventually separate causing the tire to blow out.
If it's a slow, almost rocking motion, check the tires; you probably have a "slipped belt" or a bent rim.
You should take the vehicle to the tire store where you purchased the front tires. Your description sounds a lot like either a slipped belt or a bent wheel. I'd bet on the slipped belt. Radial tires have a very flexible sidewall (radial ply) and a less flexible and tougher tread ply, called the belt. If the material between the belt and the radial plies separates, it will typically slip to one side and only in limited areas of the tire. One way to check for yourself, jack up the front end and spin the tires. Watch for an area that suddenly goes off to the side. If you see that, it's a slipped belt, and if you have a slipped belt, don't take the vehicle on the freeway and definitely get the tire replaced as soon as possible. They're very dangerous.
There should be a tension pulley that keeps the belt tight. I have used a ratchet socket to release the tension. The belt can then be slipped off the pulley. Be sure to note the way the belt is wrapped around the various pulleys before doing this. It can be confusing to figure this out afterwards.
Worst case scenario Timing belt has slipped Transmission needs service(a proffessional tranny shop can get the codes from transmission) fuel pump
check timing belt might have slipped
All serpentine belt driven water pumps on SBC engines are reverse rotation.
It has either slipped off or is broken/cracked. You need to make sure it is on properly or buy a replacement belt.
Since the Cavalier is out of timing, check the timing gears and belt. It sounds like the belt has slipped and is causing the base problem with the car.
There should be a diagram drawing on a sticker under the hood on how to replace this belt.
There is a spring loaded pulley called a tensioner that puts the correct tension on the belt. That needs to be retracted so the belt can be slipped off. I have found using a ratchet socket makes this easy to do. Otherwise you run out of travel room before relaxing it sufficiently. Make sure you know the proper routing of the belt before taking it off, otherwise you will have trouble putting the new one back on..