Yes it will always be visible. You have to a valid IP address to talk to the outside world. See how easy it is for your IP address to be seen by going here, it should display your routers IP address.
http://www.whatismyip.com/
You can use firewall's and such to help, but a router itself acts as a good firewall because your computers are excluded from view to the outside unless your start opening up ports and such. As for the wireless neighborhood issue, just use the WEP with 128bit encry and that will due good enough.
Linear Mode
