if the apartment have everything setup as they
should, It's not going to work well for you. Proper setup would have the different wireless clients not being able to see each other, chances are it's not this way.
Can you see a bunch of different computers in your finder window? then it will work for you, but unfortunately it will also work for everyone else in your building. you can password protect the speakers. although I don't think you can protect the printer, but I'm not sure.
If you can't see others in finder, then you building is setup like it should be and it won't work at all, you really don't want your neighbors having access to your computer.
you could get another router and have that act as a wireless bridge, not that hard to setup, but depending on your technical skills i would get a geek friend. It'll take maybe 30 minutes, and cost you a 6 pack.
Get a cheap router, and install
dd-wrt on it (dd-wrt is a linux based firmware, adds more features)
you'll want to check compatibility with dd-wrt before you buy, but you should be able to find one for under $50.
Then set it up as a
wireless bridge. That would get you an ethernet port that's connected to the building wifi. you would then take a cable and connect your express to that, and use the old setup.
so...
--building wi-fi--> DD-wrt
--wired ethernet--> express
--your wifi--> computer