Many times, the engine kick in to start charging the battery after I full stop and going to turn off the car. If I just turn off the car, the car will sudden shake then off. Will this good or bad for the engine? Or I should wait the charging cycle complete? Thank you.
try adding a few seconds at a time to shutting it down, and see if the shaking goes away at some point. you may not need to wait until it shuts down itself.
No, just drive it, turn it off like normal. Good chance that it's running the ICE to run the heater - which will be no use when you get out again. The battery charging (and heating) will just pick up when you start next.
I don't know why people overthink so many of these things - when you arrive you slow down, stop, put it in park, and turn the car off. We really don't need to make it any more complicated.