Newton's laws of motion — common mistakes

A common mistake is to identify two forces that are in equilibrium on a single object as an action-reaction pair. For example, for a book on a table, the book's weight and the table's normal reaction force are NOT a third-law pair. They are just two forces that happen to be equal and opposite, acting on the same object (the book). The true reaction to the book's weight is the gravitational force the book exerts on the Earth.

Not necessarily. According to Newton's First Law, an object moving at a constant velocity has zero resultant force acting on it. A resultant force is only required to cause acceleration (a change in velocity).

Because they act on different objects. To determine an object's motion, you only consider the forces acting on that object. Since the action and reaction forces act on separate bodies, they cannot cancel each other out in the force analysis of a single body.

This is a modelling assumption. We assume the string is 'light' (has negligible mass) and the pulley is 'smooth' (has no friction). If the pulley had mass or friction, it would require a net turning force (a torque), meaning the tensions on either side would have to be different.

In mechanics problems, 'smooth' is code for 'frictionless'. A smooth surface exerts no frictional force. A 'rough' surface can exert a frictional force that opposes motion or attempted motion, up to a maximum value of $F_{max} = \mu R$.