Great questions. We don't know the answers.
Certainly for many purposes the galaxy is almost a closed system, but not quite since light enters it and leaves it, etc.
What about the whole universe? For starters, we don't know if it's finite. We aren't sure what's happening at all the horizons. So we don't know if there's a way of defining any finite exactly closed system. I guess you could say "everything" is a closed system, but that would be a nearly meaningless claim, since we don't have a clear idea of what "everything" is, and we're sure we can never observe most of it.
Perhaps this is a good thing for our understanding. There's a theorem (Liouville) that in any fully closed system obeying laws of physics like the ones we know, entropy never changes. But perhaps our most general observation is that entropy always goes up. It turns out that this is what's expected from the known laws so long as there's always some "outside" for things to get more "entangled" with. So it's nice not to have to worry about systems without outsides.
Mike W.
(published on 02/26/2013)