Consider a bar magnet, and the magnetic field line that goes through its axis and through the center of its north pole and thus follows a straight line path out of the magnet. Will this line ever be reaching the south pole of same magnet?
If not, then can we say that magnetic monopoles exist?
The "magnetic field lines" are only an abstraction, not much more as an illustrative tool to explain the workings of the magnetic field.
The more exact description of the field of a bar magnet is a vector field, i.e. we have a vector in all points of the space showing the strength (and direction) of the magnetic field in that point.
The magnetic field of the bar magnets is roughly a dipole field, we have a positive pole on the north and a negative on the south (or vice versa).
This field is not defined in the poles because of a division by zero problem.
Thus, the literal answer is that no, the field line doesn't reach the south pole.
However, also this is only an abstraction. The magnetic field of the bar magnet is not generated by some magnetic monopoles in its poles. In fact it is generated by the electrons in the whole bar. The real magnetic field of the bar magnet is more complex as a dipole field. Although the field generated by magnetic monopoles would be quite similar, this is why this simplified version is taught to you.
No. If the bar's pole were a monopole you should be able to find a surface enclosing it through which the net flux is not zero. This is not the case here, when you consider the field lines inside the magnet - do take a look at the question Internal magnetic field of dipole and bar magnet.
Even if we would consider this single straight field line you mention as originating from the magnetic pole, the flow associated with a single line is zero (assuming finite field and cross section of area zero). Besides, it's common to describe these endless straight lines (as from both poles) as "meeting at infinity".
