Whereas there would be considerable acceleration, and therefore 'G force', as the stone is thrown, lasting for just a tiny fraction of a second, I can assure you that there is no residual G force whilst the body is in freefall, with the exception of the tiny air friction force.
Your further observations about controlling the vertical 'pitch' in an aircraft to achieve zero G are basically correct, as far as I could decipher. It is a delicate art to achieve the perfect pitch to maintain zero G, neither positive nor negative, and to stop the freefalling bodies inside from hitting the structure. Remember seeing things floating about in video of freefall inside those aircraft? They do move about a bit - in addition to any velocity imparted by pushing etc, and this is a visual realisation of the imperfection of the attempted parabolic trajectory.
Last edited by pilotmike; 5th December 2007 at 15:41.