Will pushing on a car always change the cars mechanical energy? what must happen for the cars kinetic energy to increase?

1) Pushing on a car will not always change the car's mechanical energy, but it does change yours since your physically using most of your energy to push the car.
 
2) In order for a cars kinetic energy to increase, the car has to be in motion when it is going down a hill, because when you go down hills and objects like that; you tend to increase in kinetic energy.