What do the six polymorphs of chocolate look like?
The actual polymorphic compound is the fat (cocoa butter). They pure phases will all look like white powders and the 'bloom' referred to in your diagram is white cocoa butter extruded by the solid chocolate, and probably the most obvious  visual difference.

The melt-in-your mouth aspect of Form V is going to be because of its appropriate melting point w.r.t your mouth temperature. The decrease in mechanical stability as the melting point decreases is fairly typical of solids (think of plastics softening as you heat them up).

Afraid I don't know why Form V is shinier.

C.f. https://www.sciencedirect.com/science/article/pii/S0969806X04003019