Isn't there a bus from the airport to plaza catalunya? If so, does it make any stops? Where do we catch it? Does it run late at night?
Yes there is. It's called the "Air Bus." See http://tinyurl.com/2r4b4p for details, and a place to click on the Barcelona urban transit system site (in english) for a map showing the route and stops. BTW, problems with the suburban rail lines, largely to do with problems surrounding construction of the tunnel for the high-speed AVE connection, mean the train line to the airport is not operating right now.