Question: I've been doing physics problems regarding cars for a while. I understand that there is a static friction (which appears when the wheel is rolling) and kinetic friction (which appears when the wheel is sliding). However, the way I'm visualizing it, static friction between the tire and road should not stop a car. In fact, when I asked this question to my teacher a long time ago, he said that it is actually the friction between the axle and the wheel that stops the car, and the road friction actually helps the car to move. But I know that when the car slips, the friction decreases and thus stopping time increases. How could this possible be linked to the axle? What is going on?

Answer: 
Have you ever tried to lift yourself up by pulling your own hair? Go ahead try it. Try it really hard. You should be able to levitate a couple of inches, right? What? You got a handful of hairs in your hand and a bald patch in your skull? It should serve you right. Hopefully, you will learn that internal forces cannot change the total momentum.

The friction of the gears, engine, etc. are internal to the car. They cannot change the momentum of the car. For all we care, replace the gears, engine, and breaks with a couple elves and other mythical creatures (a.k.a. hidden variables). As long as those hidden variables are internal to the system (car) they cannot change the momentum of the car.

If you insist that friction cannot stop the car, I dare you to drive really fast on an icy road where there is almost no friction. Hooray for Darwinism.
cars stop with their brakes, which produce friction at the inside of the wheel assemblies as the wheels rotate. This friction force retards the rotation of the wheels and dissipates the kinetic energy of the car into heat in the brake parts. 

since the wheels are in rolling contact with the pavement, and since the wheels are being slowed by the brakes, the pavement is pushing back against the wheels at their contact point with the pavement in a direction that opposes the movement of the car. So the car as a whole slows down.