The correct options are
B the free electrons move randomly in all directions
C the rate at which electrons pass through a certain cross-section from right to left to equal to the rate at which electrons pass through it from left to right
D no current flows through the conductor
If we do not apply any potential across the conductor, there will not be any external force on the electrons. So, the net motion of the electron must be zero resulting in no net current. It will only perform too and fro motion along all directons symmetrically.