Car dies at the end of exit ramps stoplights/signs

The issue with the key is because the car battery ran down. This can be compounded if you jump started it.

Check your Fuel Pressure and your Fuel Filter

well first sport mode it not meant to be pushed into operating like that. it is meant to be put into from park. it is a over drive gear not a passing gear. sounds like you may have damaged the transmission

On GM cars this type of problem was a sticking torque converter. The car acted like you had not engaged the clutch and the engine just died. You could restart it and drive on as long as it did not go into lockup.
Does it feel like that, or more like the idle air control valve is not raising the idle speed ?

O2 cause engine stall.What codes have you?

Take the car to camry automobile shop for the servicing of the car.

clean the throttle body most common cause of idle/decel die off. its cheap and real cheap and easy to do yourself

It sounds like there is a fusible link blown under the hood. The link vary in location on chrysler vehicles but they should be near the computer.

Reach in under the dash, under the steering wheel and pull the cable end off the gas peddle. Open the hood, disconnect the cable end off the throttle body, then haul the cable through the firewall from the engine side. Replace by doing the reverse.

it sound like you have a bad sensor . that control's the air & gas mix . to you carb or injector's have them checked well .good luck