Answer
(a)(i) $V_{ab} = 0 $ (ii) $V_{bc} = 0 $ (iii) $V_{\infty} = 2.25 \times 10^{6} \mathrm{V} $
(b) All are the same.
(c) $V_{\infty} = -2.25 \times 10^{6} \mathrm{V}$
Work Step by Step
(a) All the points inside the sphere have the same potential. So, the difference between any two points inside the sphere is zero
(i) $V_{ab} = 0 $
(ii) $V_{bc} = 0 $
(iii) The infinity is outside the sphere, so the potential between $c$ and infinity is
\begin{align}
V_{\infty}&=\frac{1}{4\pi \epsilon_o} \frac{ q}{R}\\
&= \left(8.99 \times 10^{9} \mathrm{N} \cdot \mathrm{m}^{2} / \mathrm{C}^{2}\right) \frac{\left(150 \times 10^{-6} \mathrm{C}\right)}{0.6 \mathrm{m}}\\
&=\boxed{2.25 \times 10^{6} \mathrm{V} }
\end{align}
(b) As we mentioned in part (a), all the points inside the sphere have the same potential.
(c) If the charge is negative, therefore, the potential at infinity is negative
$$V_{\infty} =\boxed{-2.25 \times 10^{6} \mathrm{V} }$$
