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When the current flows through the solenoid, the U-shaped iron rod will become magnetised easily and strongly.
When the current is cut off, the iron rod will lose its magnetism easily.
Iron is used as the core rod as it is a soft magnetic material, it can be easily and strongly magnetised. In addition, iron has the ability to concentrate the magnetic field lines generated by the current-carrying solenoid.
When a current flows through a wire, magnetic field is produced around the wire. This magnetic field can be detected using a compass. (compass needle is actually a magnet).
Note that the compass needle follows the direction of the magnetic field. You can use your RHGR to determine the direction of the magentic field around the wire, hence knowing where the compass needle will turn.
It fine to use a multiplug as it brings convenience. The problem arises when too many high power appliances are connected and on at the same time. The current through the multiplug cable will be too high. Due to the cable resistance, this high current results in large thermal energy generated in the cable. The rubble insulation melts and leads to fire.