(A) The amplitude is not .
(B) The direction of the velocity can be found by required that the argument of the sine function is a constant:
Increasing t a little bit requires you to increase x a little bit as well in order to maintain this equality, so the velocity in the positive x-direction.
(C) The period is .
(D) and are variables here, so this cannot be right.
(E) Consider the equation above. Let be the change in during a small time interval . Then, in order to maintain that equality we must have that
So, answer (E) is correct.