Friction on a car I wanted to ask why doesn't the car move on a frictionless surface. Suppose you are on a frictionless surface When you press the accelerator the wheels start rotating and apply a force to the ground. Then the ground should also apply force in the opposite direction, regardless of presence or absence of friction.(Third law) Or the rotating wheels don't apply any force to the ground?
But the force by the wheels on the ground should not depend on the friction of the road right?
The same thing I can ask for moving on ice. Suppose the ice offers no friction. You are standing on it. You apply some force. The ice applies the same force to you( Third law )  and you move on a frictionless ice. Where is the flaw in my logic ?
Edit 1: Many users are pointing out that I won't be simply able to apply a horizontal force to the ground. (because there is no friction). Now suppose there is some friction and I am walking on the ground. Can I apply some force greater than the limiting value of the friction of the ground? What will happen then? Please explain the physical situations and also how third law holds in each case.
 A: Without friction, neither the car’s tyres nor your foot can apply a horizontal force to a horizontal surface. They simply slide across the surface. So there is no horizontal reaction force from the surface either.
A: That's a good question, and I once had that question in my head when I was younger.
To explain you very very briefly,
First, forget about the road. Think about the air.
Air friction (or air resistance) makes things to slow down, right?
When is it air-frictionless? When there is no air.
Hence, frictionless means absence of something to interact, or simply no interactions with other things. And everything is made of atoms so I was talking about atoms.
Friction happens when atoms interact. So don't even think that we can push the ground, or even touch the ground (this is why it's a thought experiment). Pushing or touching is collisions (interactions) between atoms. If atoms don't interact with each other, the car should be just passing through the ground. And this is impossible.
My advice is, don't take things too seriously in high school. Just focus on the math. If it makes sense, then that's good enough. More will be answered in university levels.
I hope this somewhat answered your question.
A: Your understanding of the third law is correct. So there is only one question left. What kind of forces can you apply on the ground?

*

*vertical. this fine, gravity can press you down on the ground

*Horizontal. This you can ONLY do with friction. In fact this is almost the definition of friction, it’s the horizontal applied along the surface.

So the reason you can’t move sideways without friction is because that is what friction means. When you say there is no friction , what you are really saying is there are no horizontal forces along surfaces.
A: 
I wanted to ask why doesn't the car move on a frictionless surface. Suppose you are on a frictionless surface. When you press the accelerator the wheels start rotating and apply a force to the ground.

Which force? No friction = no force applied to ground

Then the ground should also apply force in the opposite direction, regardless of presence or absence of friction.(Third law)

"Opposite" to what? No force = no opposite force

Or the rotating wheels don't apply any force to the ground ?

Exactly. The friction is what turns wheels torque ("circular force") into the linear force which pushes the car. No friction = no force acting on car.

But the force by the wheels on the ground should not depend on the friction of the road right ?

The friction on the road is the ONLY thing which allows wheels to act on the road and to cause the force which phushes the car.

The same thing I can ask for moving on ice. Suppose the ice offers no friction. You are standing on it. You apply some force. The ice applies the same force to you( Third law ) and you move on a frictionless ice. Where is the flaw in my logic ?

On ice, friction is small but not 0; hence a small force opposite to the force of your feet exists and pushes you.

Edit -1: Many users are pointing out that I won't be simply able to apply a horizontal force to the ground.(because there is no friction). Now suppose there is some friction and I am walking on the ground. Can I apply some force greater than the limiting value of the friction of the ground ?

No. This is called "skidding".

What will happen then ?

Once the force of the wheels overcomes the friction force, wheels start skidding. Electronic devices mounted on modern cars prevent this from happening.

Please explain the physical situations and also how third law holds in each case.

Without friction, only throwing away a mass would result in your movement. The mass can be a bullet, or a rock,  or hot gas ejected from an engine.
