1) Usually you'd just say something like "Johnny gets (or climbs) into his mother's car (or the car)." If you want to draw attention to the fact that he ends up seated, then you could say "Johnny gets (or climbs) into the passenger seat of his mother's car (or of the car)". Strictly speaking "getting into a car" is a process but it's a very short-lived one. :) 2) "Johnny gets out of the car(, says goodbye to his mom,) and goes into the schoolhouse (or goes in to class)". Something like that. 3) "The car drives away" or "The car leaves". "The car drives off" is colloquial.

1. He gets into the car, he gets out of the car. If I'm driving down the street and I see my friend walking somewhere, I stop and say, "Get in, I'll give you a lift!" The tense depends on what is happening in the story. examples: "Every time he gets in the car, he hits his head." (repeated action, present tense) "He was getting into the car when he hit his head." (two actions at same time, in the past, past continuous+past simple) 2. He gets out of the car and goes into the school. 3. His mother drives away. If I didn't know who was driving, I might say, "The car drives away" but that sounds strange here because we know who is driving.