What would happen if I freely suspend a bar magnet at north pole, will it become vertical? I am the 8th grade kid.What would happen if earth brakes into two pieces,will there be new north and south poles developed?
You are right that the magnetic field lines at the north pole are vertical, and would be measured as such by a Dip Circle Magnetometer, which is a device for measuring the slant to horizontal of the Earth's magnetic field.
Your line of thought is sound and would be correct if the Earth were made of permanently magnetised material. However, this is not how it gets its magnetism. The Earth's magnetic field is believed to come from circulating currents within the Earth's liquid metal core. This is exactly the same phenomenon as you would see if you connected a wire between the terminals of a 1.5V battery (in series with a, say, 10 ohm resistor so that the wire doesn't get red hot) and then bring a compass near the wire: you will see that it has a magnetic field there.
The Earth (from my reading in about 2005) is thought to work as a giant electric generator: circulating currents beget varying magnetic fluxes through other circulating currents which in turn drive the first lot of current! So it's like a DC generator where the magnetic field for the spinning magnet comes from the current generated: such a generator needs a "starter" current to initially magnetise the magnetic field generating windings. Likewise the Earth is presumed to need a "starter" magnetic pulse to start this process off: when I was reading this kind of stuff in about 2005 the then theory was that magnetic fields from passing heavenly bodies (stars, possibly the Sun) would start the process off. This also kind of explains why the Earth's field flips: if you run simulations of the kind of currents and magnetism that follow from a circulating conducting metal "primed" with a magnetic pulse, a generator does indeed get running but its behaviour is chaotic: it varies wildly with time and every now and again either fizzles out (when it presumably will be started again with the Sun's magnetic field) or even flips sign. As I said, this was in 2005, and geophysics, which is not my field, may have found out more details since then.
So if the Earth broke in two: probably no, there would not be two magnets. There would a sloshing of dust and magma strewn out around the Earth's orbit, thus disrupting the whole magnetic field.