As GRAVITY is exerting a force on the astronaut, why does the astronaut feel himself to be weightless? Can the astronaut feel the difference between the weighlessness he feels in orbit and the weightlessness he would feel if gravity weren't acting on him and where could he go that he would not be affected by gravity?
I had to edit your question down a bit to fit the rules of Enotes. When astronauts are orbiting the Earth or the Moon in space, they are in an environment of relative weightlessness but they are not in a gravity free environment. The reason that astronauts feel the sensation of weightlessness in space is because there is no atmosphere to feel the effects of friction against while in motion. While on Earth, we experience the effects of gravity because our bodies are making contact with stationary objects (like the ground). Similarly, when moving through the Earth's atmosphere, we feel our bodies moving against the air molecules, thus producing friction. In space, there is no atmosphere to feel against our bodies. And because there is no wind resistance, the spacecraft and the astronauts move through space with the same acceleration, and thus one does not exert a relative force against the other. In other words, both the spacecraft and astronaut are in free fall in a vacuum.
When in orbit around a planet, an object is actually moving quite rapidly. The gravity of the planet keeps the object from moving away into deep space. The majority of the motion of the object is perpendicular to the surface of the planet. The effect of gravity keeps the path of the object in a circular shape rather than a straight line. In theory, there is nowhere you could go in space that would not have some influence from gravity, although for practical purposes if you are far enough away from a celestial body the actual affect of gravity is minimal. The astronaut would feel no difference between the gravity free weightlessness of deep space versus gravity-affected weightlessness of Earth orbit. This is because space is a vacuum, and there is no atmosphere to affect an astronaut or a spacecraft whether motionless or in motion.