Can there be a potential difference between two adjacent conductors carrying the same charge?

(A) Yes,there can be a potential difference if the sizes or shapes of the conductors are different.
The capacitance $C$ of a conductor is defined by the relation $C = \frac{Q}{V}$,where $Q$ is the charge on the conductor and $V$ is its electric potential.
Rearranging this formula,we get $V = \frac{Q}{C}$.
For a given charge $Q$,the potential $V$ is inversely proportional to the capacitance $C$ $(V \propto \frac{1}{C})$.
Since capacitance depends on the geometry (size and shape) of the conductor,two adjacent conductors with the same charge but different dimensions will have different capacitances,and consequently,different electric potentials.