Problem with potential energy & gravity.............?

You got it backwards. As the object moves up, it gains (not loses) potential energy. As it rises up, it slows as kinetic energy is converted to potential energy. The flip side is that it loses potential energy as it falls. As it falls, it speeds up as potential energy is converted to kinetic energy.

I think you're stuck partway between Newton and Einstein. In Newtonian mechanics, you can't consistently switch to the frame of reference of the moving body, because it is accelerated with respect to the fixed coordinate frame of absolute space. The Newtonian situation is as described by campbelp2002. In Einsteinian relativity, the object is freely-falling and therefore in an inertial frame. This is a perfectly resonable frame of reference in which to do the physics. You can solve the equations of general relativity in a frame in which the object is at rest in the center. But that spacetime is dynamic, and even though the object is at rest in your coordinate system, the now-moving Earth causes the curvature of space to vary with time under that fixed point. So the field strength, curvature, and its "potential" with respect to the gravitational field far away will vary with time.

The potential energy is relative. If a ball 6 feet above ground has a PE with respect to the ground( earth). SO when the earth moves and it takes the ball with it so the PE remains the same. When a ball moves upwards the PE is increased and one has to apply necessary force to increase its PE and KE. I hope this clears. Read more books. The question itself vague and wrong assumptions.