I'm not in my college campus right now. In campus we had private LAN. There my computer was directly connected to a gateway. Using subnet masks I used to find out fellow nodes on my subnet. There were tens of such subnets and we used to access internet using a proxy server, it made requests on our behalf and fetched data for us. It was a 100Mbps lan so, we got speed = 12.5MBps connection speed. Things were pretty clear.
Now, I'm at home and for the first time I'm using DSL internet connection. I don't understand how this thing works? There is something called PPPoE server and my computer being called PPPoE client. If that server is acting like a proxy, how come my IP is being shown in "what is my ip?". What about my fellow nodes? Can I trace them (I mean, find their ips). Also it shows connection speed is 100Mbps. But my plan with the provider is 256Kbps. I'm not getting speed more than 356kbps but what is this 100Mbps now? When I make a request what exactly is happening ? How is this thing working and how can get a network map of this network I'm in?
EDIT:
According to the answers, the 100Mbps is the connection speed between my PC and my modem. Well, yes it is! But there are two connection icons in my system tray. And both showed 100Mbps speed. But today, something interesting happened. The other speed changed from 100Mbps to 10Mbps:

How did this happen? What exactly is this 10Mbps.
