Hydrogen molecule potential energy graph In the above graph, I was confused at the point where the internuclear distance increases and potential energy become zero. Though internuclear distance is very small and potential energy has increased to zero.

Another question that though the internuclear distance at a particular point is constant yet potential energy keeps on increasing.

I think the point where potential energy become zero we can say that attractive forces between electron and nucleus of bonding hydrogen atoms just equals the repulsive force between bonding hydrogen electrons. It's just what I am assuming not sure either its true or not.
Normally, when the atoms are separated by a huge amount (infinity) we take this energy to be zero. Bringing the atoms closer to one another has an attractive potential and the bond has formed on reaching the lowest point on your curve.  Moving the atoms closer together increases the potential energy because here we push electrons closer to one another and this energy increases rapidly  with each small decrease in separation due to repulsion of similar charges. The slope of the curve gives the force on the atoms, so at small separation they experience a large force and repel one another. At large separation, where the slope is positive, there is a smaller attractive force.