Is there a mod where the car's engine will stop, instead of idle?

Unless your car was engineered for that operation, don't try and create some magic switch that makes it do that. you don't have a stout enough starter or battery to work that way.

You can try that out by putting the car in neutral at every stop and restarting every time you need to go. After a month of this experiment add up how much gas you saved. You will need to put that with another $300 to have a new starter put in after you wear out the one you have.

As Don R said, there are some European cars like Volkswagen that have this feature, but they still 'idle'. If I am correct, the starter motor is still rotating although it has not coupled onto the wheels, so that the car can start in less than a second, as there is still a couple hundred, not thousand RPMs going.

Your best bet would be to get a Toyota Prius engine swap. Sounds like a silly idea but it works and is great fun. Someone has already converted a bunch of cars to run on Electricity (http://www.youtube.com/watch?v=4MLLYTQYg7k)

The way that works is under a certain speed (40MPH) the electric is running, any faster and gas engine kicks in. You should do some research and then email me (MuzzaHukka@yahoo.co.uk) and I'll help you with it!

No. We all out here use the idle mode run at a stop, or drive thru. But if you want to, you can do this shut of mode thing MANUALLY.

thats actually really easy to set up. itll wear your starter out, no ac at stoplights, ton of wear and tear on the engine from all the starts, etc.

that set up is very hard on the starting and charging systems. it is also detrimental to fuel economy. the hybrids do that but it is a bit different there.

if u dont want to turn the key every time get a remote start

That is the way a hybrid works.

You have an electrical problem. Take it to the dealer of the car.