Quick questions on Specific heat capacity and latent heat: H2 Physics Thermal Physics

The specific heat capacity $c$ of a substance is the energy required to raise the temperature of $1\ \text{kg}$ of it by $1\ \text{K}$:

The specific latent heat $L$ of a substance is the energy required to change the state of $1\ \text{kg}$ of it without any change in temperature:

Heating a substance through a phase change requires adding the energies for each stage in turn: temperature change ($mc\Delta\theta$), then change of state ($mL$), then any further temperature change. A heating curve (temperature against energy supplied) shows sloping sections (temperature rising) separated by flat plateaus (state changing at constant temperature).

Define specific heat capacity and state its SI unit. [2 marks]

Find the energy to heat $0.40\ \text{kg}$ of aluminium ($c = 900\ \text{J kg}^{-1}\text{K}^{-1}$) from $25\ ^\circ\text{C}$ to $75\ ^\circ\text{C}$. [2 marks]

Explain, in terms of molecules, why the temperature of melting ice stays at $0\ ^\circ\text{C}$ while energy is supplied. [3 marks]