What is the net charge (overall or sum of charges) of the nucleus and what number is it equal to?

Because the nucleus is made up of positively charged protons and neutrally charged neutrons, and no negatively charged particles, the charge of the nucleus will always be equal to the sum of the charges of its protons. A simpler way to say it is because each proton has a +1 charge, the charge of the nucleus will be the same as the number of protons in it.