Understanding of Gauss law using vector fields I was going through the conventions and terminologies followed to describe the magnetic interactions. I understood that the field lines are just a simpler representation of the magnetic interaction described in terms of a vector field.
So those field lines basically relates to the line of force due to magnetic interactions. I hope this understanding is right.
And the magnetic flux is defined as net magnetic field lines crossing the area. And so flux indirectly relates to the magnetic forces.
After all these understandings I considered Gauss law of magnetism which states that the total magnetic flux through a closed surface is equal to zero. The observation that magnetic monopoles do not exist supports this law.
Without involving surface integrals concept (Area vector)  why can't I say If the flux is zero, Field lines are zero? And if yes Can I say that the magnetic force inside a closed surface is zero?
But this conflicts with my general understanding of the field line. Why should a close surface affect the force due to magnetic interaction?
If the surfacae integral is necessary to answer to this Question why the surface area vector is related to force vector in Gauss Law?
 A: To answer your main questions:

why can't I say If the flux is zero, Field lines are zero?

The flux through a particular area is the difference of the number of magnetic field lines pointing one way through an area and the number of magnetic fields pointing the other way. If you have the same number of field lines pointing into and out of a particular surface, then the flux will be zero even if the field is nonzero. For an analogy, it isn't correct to say: if $x-y=0$, then $x$ and $y$ must both be $0$. There are many combinations of $x$ and $y$ that will satisfy that equation, just like there are many nonzero field configurations that will give you zero flux through a particular surface.

Why should a close surface affect the force due to magnetic interaction?

Applying Gauss's Law for Magnetism closed surface is a mathematical tool that we use to describe how a magnetic field looks. It often simplifies what would otherwise be a difficult calculation; however, it is by no means the only way that we have to calculate the magnetic field (for example, the Biot-Savart Law is another useful tool). It doesn't affect anything about the field (and certainly doesn't affect the force, since the relationship between magnetic field and magnetic force is complicated).
