Capacitor having equal charges on plates connected to a battery

Hello

I am having a doubt regarding capacitors .I know that when two neutral plates of an uncharged capacitor of capacitance C are connected to a battery of V volts then charges present on the inner surface of the plates are equal and opposite i.e +Q and -Q,where Q=CV .

But what will happen when both plates are initially having a positive charge +q and then a battery of V Volts is applied across the plates ?

My doubts are

1)In general a battery supplies equal and opposite charges.Does the battery supply equal and opposite charges in this case too ,where the plates are already having +q on them ?

2) If the inner surfaces of plates of the capacitors have equal and opposite charges after the battery is connected ,then in this case the outer surfaces will carry unequal charges . Is it so ?

Please clarify my doubts ...Thanks