It falls.
the magnet will repel
When a bar magnet is held in the air by a string, it will align itself along the Earth's magnetic field lines. One end of the magnet will point north while the other end will point south. This behavior is due to the interaction between the bar magnet's magnetic field and the Earth's magnetic field.
it loses its magnetic properties
I don't see any sketch. But if you break a magnet in two, each part will be a magnet with its own north and south pole.
The compass needle would be affected by the magnetic field from the nearby magnet. The needle would align itself with the magnetic field of the magnet, causing the compass to point in a direction different from true north.
A current would be induced in the coil.
No, water is not magnetic so it would not be affected by a magnet in the same way a charged comb would attract water. The magnetic field from the magnet would not have any significant impact on the water itself.
the arrow in the compass would point to the magnet
It would spin.
Unless you scratch the disk while placing the magnet on the disk, then nothing will happen. A magnet would have to be powerful enough to extract the hemoglobin from human bloodcells to be able to effect the disk.
it wouldn't be magnet to a aluminum nail because the aluminum is not a way of magnet and a steel nail would because steel is a way of magnet.
If lightning struck a magnet, the magnet would not be affected much. Magnets are made of materials like iron or neodymium that are not easily damaged by heat. The lightning would likely dissipate through the metal without causing significant changes to the magnet's magnetic properties.