1) Can multiple players pick the same city? (I would think yes.)Correct!
2) (more important) Does this wording mean that only cards useable for completed cities can be played? (So, no play of cards like "x point(s) for houses in this province that are not in completed cities.) I'm confused about this one.
The German rules explain that you "obviously" can use Green cards to score open areas - as per usual.