Is it possible for an object at rest to have forces acting upon it

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.

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.