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.

Fuse is a safety feature. In the event of an electrical fault, where there is a short circuit current which exceeds the fuse rating, the fuse will melt and break the circuit. (fuse is blown) This will disconnect the appliance from the high potential of the live wire. The appliance will not become live and it will not be 'live' at 240 V.

Changing the pin will not change the voltage required by the appliance.

The wire used here is not the typical copper wire. It is nichrome wire which has much higher resistivity compared to copper. Hence, for the same length, the resistance of the nichrome wire has higher resistance. When the current flows through the nichrome wire, energy is transferred electically to internal (thermal) energy of the nichrome wire. The wire becomes hot so that it can cut the styrofoam with ease. This is the same concept for heating appliances like kettle etc.