Is turning off engine while driving bad?
Bad and dangerous! First, many things including the steering sytem either lock or shut down. Just about everything that uses the elctrical system is shut down...and many of these things run things, like fuel pumps, etc., that the engine needs.
What would cause a vehicle to jerk while driving down the road and after turning off vehicle it won't crank the does not crank also engine service light come on and off at the time when driving?
No...not typically. A bad PS Pump can cause a vibration while turning the wheels at slow speeds, like in a parking lot etc. Most likely a vibration while driving would be caused by, Out of Balance or Out of Round Tires / Bent Wheels or Axles / Bad Wheel Bearings / Bad CV Axle / Bad U-Joint or Damaged Driveline (RWD & AWD) Vehicles. These are the areas you should be checking first for "Vibration…