From Q1 we have,
$ \begin{align} X_8(k) &= [0,8,8,0,0,0,0,0]\text{ or}\\ X_8(k) &= 8 \delta[k-1] + 8 \delta[k-2] \end{align} $
Using the relation,
$ \begin{align} e^{j2\pi k_0/N} (u[n] - u[n-N]) &= IDFT( N \delta[k - k_0] )\\ x[n] &= e^{j2\pi (1/8)} + e^{j2\pi (2/8)}\\ k_1 &= 1, k_2 = 2 \end{align} $
