If a car shakes and loses power when idling it can be the spark plug. If a spark plug is fouling, it can cause power losses.
One thing that could be wrong with a 2013 Chrysler 200 when it loses power and smells like rotten eggs is the catalytic converter needs to be replaces. When a car has a rotten egg smell, this is usually the cause.
It means the car is overheating.
fuel filter could be clogged or the fuel pump is going out on it.
A power loss can be from a dead or almost-dead battery. If the car loses power on a hill, it might be a fuel injector or fuel pump, if I'm not mistaken.
Try changing the fuel filter.
gravity
Same as any car with power steering. You can continue to steer the car but with increased effort.
what year is your car and engine cylinders
It loses power because going uphill is harder then going downhill therefore causing it to use more gas and then making it lose power bit by bit.
If by falls in its face you mean loses all power this is normal. It is called a speed governer. It cuts your fuel once you reach that rpm. The only way to get rid of it is to remove your speed sensors or modify the ECU.
Have vehicle scanned to determine the problem