Sinbad was already being pushed away from Proteus before Marina came along.He sees her on a boat and falls head over heals to the point that he leaves everything and everyone he's ever known because he realizes that she's not meant for him? Just a bit too convenient. It would make more sense that his relationship with Proteus has been strained to the point of snapping—after all, Proteus is a prince and he is not—and Marina's arrival was just the straw that broke the camel's back. She epitomizes all that he's been realizing about class and station, as well as the distance between himself and Proteus, and so, he leaves.
Kale's actually the one running things.He must have pretty much raised Sinbad after the boy ran away from the palace, and while Sinbad is fearless, a good fighter and captain, Kale has the muscle and fear-factor that must have been necessary to command a ship of pirates. He's just too nice to let Sinbad know who's actually in charge.
Marina's famous, and the crew already knew about her before the events of the movie.They let her on the ship, no questions asked, and are quite nice to her throughout the movie. Sure, she has jewels, but it would make more sense for her to be renowned as an ambassador of some sorts, perhaps a policy-maker who fights for the rights of the poor. They know her face and name due to the good changes that she's implemented, and hence are much nicer to her than they would be otherwise.