What is the net charge on a capacitor in a circuit ? Is it ever possible for the charge on one conductor to be different than the charge on the other conductor? Explain.

zero

The plus charges on one side exactly balance the - charges on the other side.

If you for example had more plus charges on one plate then they would attract negative charges to the opposite plate and would cause a flow across. Moreover the entire capacitor would then have a net charge and would be attracted or repelled by anything charged around it.
In an old fashioned vacuum tube we had this situation for example between the cathode and the anode, but then the charges flowed across the space between and created a current even at a steady voltage, so not really a capacitor.