Question

in a bar magnet is there a line or a plane separating North and South sides of a magnet

Answer 1

There is no line or plane separating North and South poles.
Even if you break a bar magnet at the middle, you will still be getting two individual bar magnets.

Isolated North or South poles are not known to exist.

The Magnetic lines of force originate from north pole and enter the magnet at south pole. Since it forms closed loops, it travels from South to North inside the magnet and obviously, North to South, outside the magnet.