If we're staying at a Disney Resort how do we get to the restaurant?

Uber or Minnie Van is your friend

If you are not staying at Disney but visiting Magic Kingdom, do you have to pay for parking and how do you get to the park from there?

They have ferries you can take also

It depends on which resort you are staying at. It is located at the beach club so if you are staying there or the Boardwalk you can walk there. If you are at another resort you may have to take a bus to Epcot and the take a bus from there to the Beach Club.

Bus, boat or the new minnie van