A capacitor has capacitance C. Is this information sufficient to know what maximum charge the capacitor can contain? If yes, what is this charges? If no, what other information is needed?
No. This information is not sufficient. Since the charge is proportional to the potential difference across the capacitor, we need to know the potential difference applied across the capacitor.
q ∝ V ⇒ q = CV
Here, q is the charge, V is the potential difference applied and C is the proportionality constant, i.e. capacitance.