Displacement amplitude of the wave means maximum possible displacement of medium particles due to propagation of the wave, which is equal to the displacement at $B$ at the instant shown in fig. Hence $(b)$ is correct.

The phase difference between two points will be equal to $\frac{\pi }{2}$ if distance between them is equal to $\frac{\lambda }{4}.$

Between $A$ and $C,$ the distance is less than $\frac{\lambda }{2}.$ It may be equal to $\frac{\lambda }{4}.$

Hence, phase difference between these two points may be equal to $\frac{\pi }{2}.$