Wireless router help

So, I tried googling for about a half hour, but then realized the world of wireless networking is incredibly complex, so I was hoping to just try here and see if anyone can help me out.

I live in an apartment complex, where, as far as I'm concerned there are a few routers across the place. I don't know how commercial internet works, but I know that there are three wireless networks in the complex.

I guess my first question is, can multiple routers contribute to the same network? So if I connect to a wireless network, is it possible that multiple physical routers all transmit a signal for the same network?

I ask this because, the other day when the internet stopped working, the apartment staff sent out an email with some general tips. I live in one of the few rooms that has a router, and so I decided to unplug it and plug it back in, to see if that fixed anything. Now, when I unplugged the router, none of the three wireless networks to choose from went away, according to my mac. Thus, plugging the router back in didn't change anything either. Upon looking at the router, the ethernet cable is plugged into "port 4" and nothing is plugged into "internet"...

So my only guess is that maybe some other router has the 'internet' port being used to connect it to the wall jack, and other routers where the cable goes into 'port 4' are helping contribute to the same network and all broadcast the same signal? I hope this made sense, please let me know if I need to clarify!

If this isn't true then, then perhaps if I plugged the cable into the 'internet' port instead of 'port 4' it would do something... but I don't want to fiddle with it and somehow be in trouble with management. But if the router that's in my room isn't doing anything (not transmitting) then I'd want to fix that of course.