If Northern Hemisphere compass points to magnetic north and this same compass is brought to the Southern Hemisphere, will the 'painted red north' compass needle be drawn to the magnetic south pole?
If you keep 2 bar magnets together opposite poles attract. We all know that. A freely suspended bar magnet will also align with Earth magnetic field. Earth is a big magnet and needle in the compass is also a magnet.
If you think the Earth's magnetic north is north pole then the needle in the compass with red Mark should be south pole and vice versa. That is why they attract and needle in compass with red end point should always point Earth north pole irrespective of which hemisphere.
Magnetic compass usually come with error, manufacturers will specify error correction table based on your position on earth. Magnetic compass maybe reliable up to 70 degrees latitude but as you move close to poles the compass is of no use. That is why aircrafts fly in polar regions do not rely on magnetic compass. I hope this answer helps.