Hey and welcome!
Which key are you using to board the ship? If you can see the ship on the overworld you should be able to board it. It's 'Shift' or 'Z' key (configured as the 'A' key in the Gamepad config). While on board to get into the cockpit using the same key as Menu and to disembark press Shift again.
As for the secret character...did you do Kumo's shopping list? That will point you in the right direction ;) (you don't need to have done it to do the quest though!)