Yes
No.
A car with an automatic transmission.
If the automatic transmission car jerks when accelerating and the dash does not indicate a gear, there is a problem with the transmission. Check the shift solenoid.
You will have to get your car repaired. There is no way to tell exactly what is wrong with your car without actually looking at it.
No, No car equipped with an automatic transmission should, unless the linkage is out of adjustment and it is not going into park.
would an automatic transmission car jerk when shifting after having had a transmission flush
A car with an automatic transmission. Or an automatic. (same thing)
No but, be sure it has come to a complete stop before you put it in park.
A parts car like yours with an automatic transmission.
There are many benefits of owning a car with automatic transmission. These benefits would include the automatic shifting of gears as the vehicle moves.
Manual cars can be started with a bad starter due to the ability to roll start the car. Automatic transmission cars are not so lucky. To roll start a manual car all you need to do is put the car in gear with the key in the "on" position, push in the clutch, get the car to roll, then quickly release the clutch. The transmission will slam into the engine and force it to turn. Don't forget to push the clutch back in once it starts or the car will stall.
It means that you do not have stick shift in your car, your car shifts gears for you, you don't have to do it, so basically if you don't have a stick shift car you have an automatic transmission car.