How do tyres actually push a car forward?

Say a wheel is going to rotate in a clockwise direction and move in the right hand direction. Now i have learnt that static friction causes the wheel to move in the right hand direction. The explanation i was given for this is that friction opposes relative motion between the tyre and the ground and so when the wheel attempts to rotate in an anticlockwise direction- the friction causes a force to be applied on the ground in the left hand side direction. According to newton's 3rd law an equal and opposite force should be applied on the tyre by the road in the right hand side direction.This is hence the tractive force that pushes the tyre forward. My doubt with this is that since this force acts on the bottom of the tyre(since it's a product of frictional force) shouldnt this force applied on the tyre on towards the right cause a torque that opposes the spinning of the tyre?(If a body is rolling clockwise and a force is applied on the bottom towards the right then a torque is applied in a direction opposite to the rotation). Hence doesnt this force that was supposed to push the wheel forward just oppose the torque applied from the wheel?

My original solution for this was that since the wheel is a body that is not only pivoted but free to move in the direction of the force- If you consider the wheel to simply be a freely moving rigid body then it doesnt matter where the force is applied- all that matters is that friction was applied to the right hence it causes translatory motion. But this brings me to my final question: If you have a wheel that is free to move front and back and also allowed to rotate freely- if i applied a force on the bottom of the wheel, would that cause the wheel to rotate or to move forward?