How does the opening chapter of Rebecca set up characterization, settings, character relationships and themes?
This is an interesting question to think about because, actually, the first chapter of this classic by Daphne du Maurier actually witholds information more than it supplies us with details such as you are wanting to focus on. Its purpose is to tantalise and to increase anticipation as we think about what could have happened to have changed the situation of the narrator so drastically. Clearly, the major item that is introduced, so much so that you can almost call it a character in its own right, is Manderley itself, but, as the last lines of the chapter say:
We would not talk of Manderley, I would not tell my dream. For Manderley was ours no longer. Manderley was no more.
The happy memories of Manderley and the way that it and the happiness associated with it are completely lost, so much so that the narrator says "There will be no resurrection," cause us to wonder what on earth could have happened to this location and to the relationship of the wife and husband who are now travelling around various countries and reminding themselves of echoes of their former life.
Thus the function of the first chapter, by starting off in the future at some unspecified time, is to increase our interest in the rest of the novel.