$(A-D)$ $(i)$ Rigidity: $Gas < Liquid < Solid$
$(ii)$ Diffusion: $Solid < Liquid < Gas$
$(iii)$ Compressibility: $Solid < Liquid < Gas$
$(b)$ $(i)$ Expansion of gas: Gases expand upon heating because the kinetic energy of the particles increases, which overcomes the interparticle forces of attraction. This allows gas molecules to move randomly in all directions and exert pressure on the walls of the container.
$(ii)$ Compressibility of gas: Gases have very weak interparticle forces of attraction and large intermolecular spaces. Therefore, when external pressure is applied, the gas particles are forced closer together, significantly reducing the volume and potentially leading to liquefaction.