Question

how does the magnetic compass show its north as the earth's north contradicting the law 'like poles repel and opposite poles repel'.....

Answer 1

North pole is actually a South seeking pole

All magnets have a north-seeking pole (abbreviated to just north pole or N). It is the end that points north. This is often coloured red on a magnet or compass.

The opposite poles of two magnets attract. Therefore, when the red end of a magnet or compass is pointing north, it is because it is being attracted in that direction by the south end of another magnet (often coloured blue) – this is the imaginary magnet inside the Earth.

So, when we think of the Earth as a big magnet, it is the blue south pole of the magnet that is underneath the North Pole of the Earth (note the use of capitals for the place and lowercase letters for the magnetisation).

In summary…
There is a direction, north; the north poles of magnets line up with this direction. And the North Pole (note the capitals) is a place on the Earth towards which all compasses point. Therefore, unfortunately, the magnetisation of the North Pole and the north-seeking pole must be opposite to each other – because they attract.

To add to the uncertainty . . .
Geological records suggest that the Earth’s magnetic field actually flips roughly every 200,000 years, so the North Pole may one day become a north-seeking pole