Jack Campbell, Fat Cop and Cheeseburger Doyle are the same person.
He transformed into a talking cheeseburger through some sort of curse or karmic twist, vowing to give up his gluttonous ways. Fran is Kiki's hostage.
The theme song implies that Kiki purposely plowed into Fran's boat on purpose, and Kiki manages to rebuff any rescue attempt. Despite her facade of cluelessness, Kiki still is the more active one of the duo, and she seems to know enough about the island to keep herself and Fran alive and relatively comfortable. She stranded Fran with her with the plan to keep the other girl on the island as her friend forever, and ever.