The only thing that a net force in the positive $x$ direction means is that the net acceleration is in that direction. It tells you nothing about its position or velocity.

a) Imagine placing the $x$-axis vertically and letting the positive $x$ direction be downward. Now imagine that the constant force is gravity and the particle is a ball.

If you throw the ball upwards, it has a negative velocity (so it is moving in the negative $x$ direction) but it has a positive acceleration.

b and c) These relate directly to the analogy described above. An object moving upward experiences slowing down (an acceleration opposite the direction as velocity), while an object moving downward experiences speeding up (an acceleration in the same direction as velocity).

d) Assuming the problem really does mean "net force", the total sum of forces acting on the object, you are correct on this one.

The only thing that a net force in the positive $x$ direction means is that the net acceleration is in that direction. It tells you nothing about its position or velocity.

a) Imagine placing the $x$-axis vertically and letting the positive $x$ direction be downward. Now imagine that the constant force is gravity and the particle is a ball.

If you throw the ball upwards, it has a negative velocity (so it is moving in the negative $x$ direction) but it has a positive acceleration.

b and c) These relate directly to the analogy described above. An object moving upward experiences slowing down (an acceleration opposite the direction as velocity), while an object moving downward experiences speeding up (an acceleration in the same direction as velocity).

d) A net force in the $x$ direction will have no effect on velocities in the $y$ direction, so the particle's motion in the $y$ direction is independent of its motion in the $x$ direction. The particle can be moving in the $y$ direction.