1) Should I just start the car and leave it idle and restart if it turns off (and do this till 2-3 tanks of fuel has been burnt)?
Break-in involves running the engine in a rich needle setting at low throttle for the first few tanks (2 to 4). It is common for the engines to quit a few times during break-in, so just restart it when that happens. Many people do the first tank stationary, but the subsequent ones can be moving, but at low throttle.
2) If the above is true, I am not sure if I can do this because the car (the way it is tuned at the moment) still moves even in idle mode. What can I do about this?
That means your low endpoint for the throttle is a bit high, you should be able to use your transmitter trims and/or endpoints to bring it down.
3) Do I take the car to a free parking area or something and just run the car at slow speed till I burn 2-3 tanks of fuel?
In any case, how would I know that the break-in is complete?
That is not a bad idea, for your second tank onwards. If it is a model with brakes, that will also help to keep it stationary. There is no hard rule about when break-in is complete, follow the instructions in the engine manual (if any). Otherwise, you can slowly start leaning the engine (using the high speed needly primarily) after the first couple of tanks.
I am not much of a car person, and my advice is primarily based on the general nature of glow/nitro engines.
Hopefully the car folks here will respond in more detail.