Answer
(a) $\Phi_{E} = 1.8 \mathrm{N} \cdot \mathrm{m}^{2} / \mathrm{C}$
(b) Independent
(c) (i) The largest value when $ \phi = 0 $ (ii) The smallest when $ \phi = 90^o$.
Work Step by Step
(a) The electric flux is calculated by
\begin{align}
\Phi_{E}& =E \cos \phi A\\
&=(14 \mathrm{N} / \mathrm{C})\left(\cos 60^{\circ}\right)\left(0.25 \mathrm{m}^{2}\right)\\
&=\boxed{1.8 \mathrm{N} \cdot \mathrm{m}^{2} / \mathrm{C}}
\end{align}
(b) The electric field doesn't depend on the shape of the sheet as it is a flat sheet and the electric field is uniform over it.
(c) (i) The largest value of $\Phi_{E}$ is when the angle $ \phi $ is zero where $\cos \phi = 1$
(ii) The smallest when the angle $ \phi $ is $90^o$ where $\cos \phi = 0$
