Car engines are demanding and require proper care to be taken. Failure to do so can result in problems with fuel, ignition, emissions, and other various systems. A vehicle is said to be idling when it has sufficient power to work the steering or other components but not enough to move the vehicle itself.
It is idling. This is hard for an engine to do smoothly.
moving
There are many reasons why your car might vibrate while it is idling. It could be running too hard for example.
The power steering pump is working hard and the engine is only idling. It could be the harmonic balancer
Possibly due to engine mount
Idling too high?
Loose motor mounts.
If the car dies while idling, the timing might be off. Other causes can include a clogged fuel filter or a bad spark plug.
loud, and shety muffler
could be a broken engine mount.
It is more than likely a thermostat
Could be time for a tune up.