Some hints for this problem: if E[X] = 0, then Var(X) = E[X^2]

Cov(X,Y) = E[XY] - E[X}*E[Y]

correlation coeff = Cov(X,Y) / sqrt(Var(X))*sqrt(Var(Y))

X & Y independent: E[XY] = E[X}*E[Y] ie Cov(X,Y)=0

try to express your answers in terms of given constants rho, sigma_x, sigma_y