Balanced force:-
If the resultant force acting on a body is zero then it is called balanced force.
Balanced forces do not cause a change in motion. They are equal in magnitude and opposite in direction. Therefore, the resultant of these forces will be zero.
Example: Two persons pushing a box with the same force in opposite directions.
..
Unbalanced force:-
If the resultant force acting on a body is non-zero it is called unbalanced force.
Forces whose resultant is not equal to zero are called unbalanced forces.
Example: An arm wrestling competition among a strong person and a weak one. The resultant force will be in the direction of the force applied by the strong person.
..
Yes, a body can move with a non-zero velocity if net force acting on it is zero. Here it will move under zero acceleration and in normal conditions would eventually come to rest.