1.) The pen is at rest. The pen is at rest because the forces, tension force and gravitational force, are balanced.
2.) Yes. There are forces acting on the pen, the gravitational force which is the downward force and the tension force found in the string holding the pen which is the upward force.
3.) The pen falls to the ground - moves downward. The cutting of the string is the reason why the pen moved, because of the cut, the tension force on the string is also removed from the pen, causing the gravitational force to prevail, causing an unbalanced force, causing the pen to move downward.
4.) The book is at rest.
5.) Yes. There are forces acting on the book, the gravitational force which pushes the book downward and the normal force exerted by the table to the book which pushes the book upward. These forces are balanced that is why the book is at rest.