risk aversion and convexity of indifference curve
It would seem that both options are correct given the specific mean-variance utility function.
Use $\mu$ to denote the expected value. In the $(\sigma,\mu)$-plain, an indifference curve representing a particular utility level $\overline U$ is given by
\begin{equation}
\overline U=\mu-\frac12 A\sigma^2.
\end{equation}
Applying implicit differentiation, we can obtain the slope of the indifference curve to be
\begin{equation}
\frac{\partial \mu}{\partial \sigma}=A\sigma,
\end{equation}
which is increasing in $A$, the parameter of absolute risk aversion. This shows that option (a) is correct.
Moreover, if we measure the degree of convexity of the indifference curve by the value of its second derivative, we'd get
\begin{equation}
\frac{\partial^2\mu}{\partial \sigma^2}=A,
\end{equation}
which is again increasing in $A$. This suggests that option (b) is also correct.
This conclusion seems consistent with the graph you show: within risk aversion, the indifference curves with higher curvature are also the ones with steeper slopes.