"3.) By Newton’s 3rd Law, a train pulls backward on its engine exactly as hard as the engine pulls forward on the train. Since Newton’s 3rd Law is correct, the force of the engine on the train should be equal and opposite to the force of the train on the engine. Therefore, the train shouldn’t go anywhere. Carefully explain why this analysis is wrong."

The force is applicable according to the newton's third law of motion but the force on the engine is compensated in the form of stess on the fixed parts and rigid links whereas the wheel is free to roll.

Explanation:

This interpretation that the engine applies a force on the train and the train also applies an equal force on the engine and hence the train should not move is wrong because the engine imparts a rotational force in the form of torque on the train and the train imparts an equal force on the engine in the opposite direction but the engine is fixed like a structure on the chassis of the train and consists of rigid links which resist the motion and deformation as compared to the relative motion between the wheels and the rail tracks.