Answer
No. No.
Work Step by Step
Even if the net force on a system is zero, the net torque can be nonzero. See the top diagram. The net force is zero (the forces cancel), but there is a net torque about the center of the rod that would start it rotating.
Even if the net torque on a system is zero, the net force can be nonzero. See the bottom diagram. The net torque is zero (the object wouldn’t start rotating), but there is a net force that would accelerate the object linearly.