All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
a and b are either zero vectors or parallel to each other.

(ii)
From (i)
$\hat{n}= \frac{1}{\sqrt{1+2^{2}+2^{2}}}\begin{pmatrix}1\\2\\-2\end{pmatrix}$

(iii)
$cos{\theta}=\frac{|\begin{pmatrix}1\\2\\-2\end{pmatrix}{\bullet}\begin{pmatrix}0\\0\\1\end{pmatrix}|}{\sqrt{9}}=\frac{2}{3}$