Curvature of electrostatic potential is zero

The electric potential $\phi:\mathbb{R}^3\to\mathbb{R}$ is the solution to Laplace's equation and therefore a harmonic function. Harmonic functions enjoy several nice properties, some of them listed on the Wikipedia page.

Concerning OP's second point, let us mention that there is a theorem similar to Liouville's theorem from complex analysis that a bounded harmonic function defined on the whole $\mathbb{R}^3$ is a constant function .

Concerning OP's first point, Zangwill is looking at the graph

$$ {\rm graph}(\phi)~=~ \{({\bf r}, \phi({\bf r}))~\in~ \mathbb{R}^4\mid {\bf r}\in\mathbb{R}^3 \} ~\subset~ \mathbb{R}^4 .$$

The graph of $\phi$ is a 3-dimensional submanifold with possible curvature embedded in $\mathbb{R}^4$. The metric on the graph is induced from the standard metric on $\mathbb{R}^4$.