(A) The thermal conductors don't have to be hot to transfer heat, as when the case of ice cube is taken, when the ice cube is placed in the warm water, it melts because the thermal heat from the warm water move into the ice cube, the thermal energy of the ice cube increases whereas the thermal energy of the water decreases.
(B) A heat transfer medium is may be presented in the solid, liquid or the vapor phase. It is used to transfer heat from one place to another or to store heat in a reversible form.
(C) Option A is correct.
This is because, the magnetic field lines transfer from North Pole to South pole which is the correct origination and the destination respectively.
Option B is not correct because the magnetic field lines originate from North Pole but does not end at the South Pole.
Option C is not correct because the magnetic field lines cannot travel from the same pole to the another same pole of the magnet. In this, the magnetic field lines originate from the South Pole and ends at the South pole of the other magnet which is not possible.
(D) The law of conservation of energy states that energy can neither be created nor destroyed, it can only be transformed from one form to another. A heat pump is a device that can pump thermal energy either into (heating) or out of (cooling) an enclosed space, which means system remains the same but the heat gets converted from one form to the another.