I just noticed: When I'm hiding the drawer via toolbar button, the drawer's visibility is indeed remembered. Sorry. Closing the drawer manually (i.e., dragging its edge, and that's what I had done) doesn't have the same result, though.
Re: "drawer is opened on the side of the window where it fits best": Cyberduck appears to prefer the left edge -- I had expected the drawer to stay on the right side once I had forced it to open there. But that's probably a deliberate design decision, so I won't argue ;-)
Bookmarks drawer doesn't remember its width between window spawnings.
I don't know if this is due to the 'default' behavior of Mac OS X's drawer UI, but, it would be nice if CyberDuck did the work necessary to maintain some preference for Bookmarks drawer width -- as well as orientation (left edge / right edge) -- and then, whenever spawning a new window, implemented those prefs.
(Of course, an elegant seamless implementation would be best, but I'd prefer this behavior even if it 'looked ugly', i.e. screen flashes while cyberduck 'corrects after the fact' OS X's default behavior (prefer left edge, wherever fits, 'standard' width).)