Answer
A spacecraft would have to travel infinitely far from the earth in order to escape its gravitational pull.
The spacecraft would not remain in orbit if it was not influenced by earth's gravity.
The astronaut in orbit feels weightless since the centrifugal force cancels out the graviational force.
Work Step by Step
Since gravity is an infinite range force, it is not possible to escape the gravitational pull of the earth no matter how far one travels.
If the gravitational pull of the earth on a spacecraft was somehow turned off, there is no longer a source of centripetal force required to maintain the closed orbit. Thus if the spacecraft is not under the earth's gravitational influence, it cannot orbit it.
Astronauts in orbit around the earth are in a rotating frame of reference, which is not an inertial reference frame. Due to the acceleration of the frame of reference, the astronaut feels a pseudo force in the form of centrifugal force, which is equal and opposite to the gravitational force exerted on them by the earth. Thus in orbit, the astronaut has 0 net force acting on him( since gravity and centrifugal force are in opposite directions, they cancel out) and thus he feels weightless.
