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Check your power steering fliud, if it is low this could cause the vibration you are feeling.
inspect the upper motor mount
Try changing the ignition switch located on the steering column
Loose or worn out power steering drive belt. Usually this is a loose or worn belt on the power steering pump. The pump works its hardest when the vehicle is parked or at low speeds so if there is a belt issue, it will happen then.
i was told its because they are for when you are parked only, and if you drive with them on someone could mistake that you're parked and hit you.
Your 4 wheel drive may be engaged. Take out of 4 wheel drive and put it in reverse. Drive the car in reverse while turning the steering wheel all the way from one side to the other until it disengages.
it will drive but when in reverse it wont move
The squeak is your tires losing traction on the pavement. Prominent in rear wheel drive cars.
Drive or if you are parked, sleep.
It is not illegal to drive without power steering. Many people who drive very old cars do not have power steering.
Most likely issue is a motor mount collapsed. The second most likely is a misfire.
that sounds like your transsion you should have it looked at although you can drive it with out reverse for quite a while