Idle speed fluxating

lift the bonnet and look for the obvious, like a broken drive belt
to the alternator etc
If you damaged the engine it will be rough running , banging itself apart, smoking so from your description, poor as it is I would be looking for ancillary parts failure, tire failure , cv joint failure or something like that

The idle speeds software driven But vacuum leaks can raise idle speeds or weak mounts cause the shift in position giving you the jolt.

sounds like forward pump seal in transmission failure

Time to see the Audi dealer I think. One suggestion, are you using AUDI factory replacement parts?

There is no idle adjustment on a 1996 Buick LeSabre. The idle speed is computer-controlled. Incorrect idle speed can be caused by many things including a faulty Idle AIr Control (IAC) motor, vacuum leaks, or malfunctioning sensor inputs or circuits such as the Throttle Position Sensor (TPS). If it is not idling correctly, the engine control system must be properly diagnosed to find out the reason why.

Below is the diagram you requested. Best of luck!

1996 Buick Riviera Serpentine 3.8

would change top hose plus make sure there is a thermostat fitted

Replace the idle speed control and check the TPS voltage

Do you have a check engine light on? First thing I would do is unplug the IAC motor when the engine is warm. If the idle speed doesn't change you have a vacuum leak or a bad IAC motor. If the idle speed goes down you might have a bad TPS or IAC

Your engine coolant is what your heater gets the heat from. You need to start your car and let it warm up for awhile before any heat will come. This is how most cars heaters work. Yours sounds like it is working fine; most cars take a little while to warm up.

Hope this helps!