Question

Can we give as much charge as we wish to a capacitor??

Answer 1

No, the reason is as follows
The equation of the capacitor says Q = CV.
Hence one can increase the amount of charge by increasing the voltage across the capacitor.
But there is a limit, if the voltage will be increased beyond the dielectric breakdown limit, the dielectric material between the plates will become conducting and the charge will start dissipating.
One may say that such thing cannot happen if we do not place any material at all i. e. vacuum, then no current can pass.
But in this case the phenomena of field emission will be an obstruction. Extremely high electric field will make electrons leave the metal plate( similar to photoelectric effect), and hence charge will dissipate.
So there is always an upper limit to the amount of charge that can be given to a capacitor.