1) I think maybe Tiko Tiko around the island cruise stops at Happy Bay. If not, Paul's nude cruises definitely do. They can make arrangements to pick you up.
2) I suggest you make advance arrangements with a cab driver, as there MAY be cabs by Pedro's, but I wouldn't count on it, especially if there are no ships in. You could call TTOL sponsor Wilfred Brooks and set something up.
3) You could check with our sponsors here, but for one day, I know they do some car rentals directly from Club Orient.