Pretty basic stuff, but to be honest I haven't found a circuit diagram showing a capacitor discharging in parallel.

The only scheme I can come up with is shown here: $\color{gray}{\textbf{[ Edited ]}}$

I'm assuming a fully charged capacitor at $t = 0$

However the parallel one actually looks like the one in series. The only difference appears to be that Capacitor and Resistor have change placed, but current should still flow as if they are directly connected in series circuit.

$\textbf{So: Is there any way a capacitor can discharge in parallel?}$

Also depending on on what circuit it leads to different formula:

$$\begin{align}\textsf{[discharging]} \\[12pt] \textbf{Series:} && 0 = U_R + U_C & \Rightarrow & 0 = R\,\dot{Q}_C + Q/C \\[12pt] \textbf{Parallel:} && I = I_R + I_C & \Rightarrow & I = U/R+ \dot{U}\,C \end{align} $$