Can residents of Gaza and the occupied West Bank vote in Israeli elections, when they are under Israeli rule? If the answer is no, then that's apartheid.

You're not making the Israeli-Palestinian Conflict better. You're making the word "apartheid" meaningless.

Do they want to vote in Israeli election? Do they even want to live in a democracy, let alone in a binational country together with Israelis?

That is occupation for you. Could residents in Iraq and Afghanistan vote in American elections, when they were under American rule?

Can they vote in their own local government (Hamas and Fatah)? If no (it is) does that make them apartheid?

Double standards or ignorance.