Does an object possess force

Answer 1

When drawing a free body diagram, it is incorrect to draw any forces an object exerts on itself.

There are several forces that can be confused with an object exerting force on itself, such as the force of gravity and the various forces involved in structural integrity.

The various parts of a large machine or other physical thing certainly can exert force on each other.
For example, a typical flashlight has a spring that presses against the batteries with some force, and the other end of the batteries press against a metal contact with roughly the same force.
However, all such forces are balanced. The net force on the object as a whole is always zero, so the net acceleration to the center of mass caused by such forces is always zero.
So when you only care about the object as a whole and how it interacts with external objects, you draw it as a single object in the free body diagram and ignore all such internal forces, since their total net force is zero.

When you do care about internal forces of a large physical object, for example the structural integrity of a bridge, you draw each part you are concerned about as a separate object in the free body diagram.
Perhaps you will draw each strut in a bridge truss as a separate object.
With such a more detailed diagram, one can calculate the forces between parts of the bridge, and find the appropriate size strut and bolt to handle those forces.
The extreme case of dividing up a large physical object into smaller parts on a diagram is called finite element analysis (FEA).
People doing finite element analysis make free body drawings that show "objects" that correspond to small, in some cases microscopic, regions of a solid strut or bolt.

Some Science Fiction writers describe spacecraft that somehow "pushes itself" from one place to another, using "reactionless propulsion".
But as far as we know now, all such devices are purely fiction. All known methods of moving a person from one place to another require forces on some external object.
Walking and taking the train push directly against the Earth; airplanes push air down and back to provide lift and thrust; rockets push propellant out the rearward-facing end of the rocket, etc.

Answer 2

The answer is yes, according to Einstein's theory of general relativity E=MC2, any object with mass will have energy. The more mass, the more energy.