Yes, it is possible for an object at rest to experience force. For example, a book on a table may be at rest, but the book has gravity acting upon it, as well as the force from the table.
Yes. As stated in the other answer, if a book is lying on a table, it still has forces acting upon it known as the force of gravity and the normal force. These forces balance each other out which explain why the object is in equilibrium.
