(11) FALSE
To get E from V, we need to differentiate V with respect to a coordinate which points along the component of E that we are interested in. Thus we need to know the slope of the graph of V vs. that coordinate, which cannot be found from a single point.

(12) FALSE
The E field is zero inside a conductor which carries a static electric charge (as shown in the chapter on Gauss' law), but that requires the potential to be constant everywhere inside the conductor.