Is it possible for an object to be travelling with a non-zero velocity if the object experiences a net zero external unbalanced force? If yes, what is the magnitude and direction of the velocity of the object?

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Solution

Yes, that is certainly possible. We do not need for force to be acting on a body for it to be traveling with some velocity. This one of the standard deductions made under classical mechanics. In ideal conditions, force is not required to sustain a bodies velocity but it can alter it.
In a frictionless, vacuum environment a body will move with the same velocity it started out with, with no force acting on it.

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