Question

As $C=\left(\frac{1}{V}\right)Q,$ can you say that the capacitance C is proportional to the charge Q?

Answer 1

No. Since capacitance is a proportionality constant, it depends neither on the charge on the plates nor on the potential. It only depends upon the size and shape of the capacitor and on the dielectric used between the plates.
The formula that shows its dependence on the size and shape of the capacitor is as follows:
C = $\frac{{\in }_{0}A}{d}$
Here, A is the area of the plates of the capacitor and d is the distance between the plates of the capacitor.