Will it harm an automatic transmission car if you switch it into neutral while the vehicle is still moving?

It won't hurt anything, but it is stupid and pointless. If you think you are saving gas you are wrong. That actually makes the car use more fuel. It is actually better to keep the transmission in gear since on modern fuel injected engines the fuel injectors shut off when you lift off the gas pedal - except when the engine is idling, which it would have to do if you were in nuetral. With the transmissoin in gear the revs will keep the engine running without opening the injectors.

There is a trade-off. Shifting into neutral removes engine braking from the drive train. Any fuel savings will be used up when you have to get a brake job because you may have to use your brakes more if the traffic in front doesn't start moving when you arrive. Other than that, I know of no damage.

watch your rpm's (if you have a tachometer)......once you are down to about 500 to 1000, and almost stopped, shifting to Neutral shouldn't damage your transmission. This method can be used to prevent drive wheel spinning at an icy intersection, for example. Shifting to Neutral with the clutch depressed in a manual shift vehicle will cause your vehicle to move faster. Shifting to a lower gear in a Manual Shift vehicle will brake the engine and cause it to slow down. In an Automatic transmission vehicle, you will need to come off the accelerator sooner and brake gently in order to slow down, Shifting to Neutral when stopping is a personal preference, similar to shifting to Neutral in a manual transmission. You also don't need to press that button on the Automatic shifter in order to shift from Drive into Neutral. This prevents you from accidentally shifting into Reverse in an Automatic transmission vehicle

I hope that helps you somewhat.

No. However, it is illegal in many places. Also, if the person accidentally overshoots the neutral position and puts it in reverse or park, that will damage it. Finally, because of the lack of "engine braking" when in neutral, the person is more likely to crash the car, which will damage it.

Not at all, I've done it pulling in to parking spots often enough. Although what you are describing is technically illegal, you aren't allowed to coast(and you admit that is what you are going) in most States. To be fair it's unlikely that a cop will notice.

Wont hurt the tranny, but you ARE causing the brakes to wear faster.

Lots of people think they are saving gas by coasting. Maybe they are, but at a cost.

Yes, it will harm the tranny. The shafts and plantary gearsets will move without lubrication. Stay in drive.

won't hurt it, but I think it's illegal, but you aren't trying to do wrong, you just made a mistake

if your foot is still on the gas, yes. other wise, no.