Why is it better to keep the wheels of a car rolling rather than locking up while applying the brakes?
This is because when the wheels are rolling, the friction that acts between the wheels and surface is static friction. When the wheels are locked kinetic friction acts between the two surfaces. Since the value of static friction is higher than kinetic friction it is better to keep the wheels of the car rolling.
Magnetic fields do no work. Then how is an electromagnetic crane able to lift iron pieces, since work is done in lifting the pieces.
In this case work is definitely being done but not by the magnetic forces but by the electric forces. The magnetic force does the job of redirecting this electric force which can do work.
Will the Center of Mass and Center of Gravity be at the exact same point for an object lying on the surface of earth?
No. The center of mass is related to mass and the center of gravity is related to weight. Center of mass is a point at which the distribution of weight is equal in all directions. It can be thought of as a point where all the mass of an object is concentrated. Center of Gravity is the point where the the gravitational force acts. It is slightly lower than the center of mass for an object lying on the surface of earth because the the force of gravity is different for different points on the object. This is due to the non uniform gravitational field of earth which decreases as we move away from the surface of earth. In a uniform gravitational field these two points coincide.