In a complicated system like the drive to car wheels, at every point of contact between the parts, N3 applies and you can choose a force in either direction. The effect on the car is to slow it down (of course) and it is fruitless to spend too much time looking for a paradox; there is not one. More than 20 posts on this thread is evidence that this approach just generates confusion.static friction force tends to accelerate the braking wheels rather than slow them down.
I made the point much earlier that everything can be resolved with a diagram (and I haven't seen one on this thread) which includes all the forces with and without slipping. Rather than demanding a resolution to this question, people who have a problem should really sit on their own with a paper and pencil and figure it out independently. Intuition can easily fail you in a case like this
This is not strictly right. But it's really a matter of how you are defining things. Are you referring to acceleration of the CM of the wheel, or to its rotational motion? If there were no friction, the wheels would be travelling forward (rotating or not; that's irrelevant). Friction contact with the ground would, of course, tend to cause peripheral speed (relative to the axle) of the wheel to approach the translational speed of the car. Assume that the wheel is massless. The only forces will be due to the force on the mass of the car, acting through the axle. Take an instantaneous fulcrum, half way between the contact point and the axle and you have equivalent forces slowing the car and forcing the wheel to rotate.
If the wheel has mass (moment of inertia, actually) and not rotating, but moving forward, when dropped onto a surface with finite friction, there will be a backwards force on the contact point until its rotation speed reaches the linear speed. But there will be a transfer of linear KE to rotational KE, which will slow up the wheel. You could say that you have 'sped up' the wheel by making it rotate - but have you?