On a WGR614v6 you can view the WEP keys by logging in to the router and clicking "Wireless Settings" under "Setup". While you're there, it would be best to change the Security Option from WEP to WPA (WEP has been cracked).
That depends on the router. Consult your manual. Most routers sit listening at http://192.168.0.1 or http://192.168.1.1 (although there are many other possbilities). When you open the URL in your browser, you will get a prompt to log in, then you provide the userid and/or password configured for your router. Since you haven't said what router you are using or how it was setup, we really can't be more specific.
It works on most Netgear routers, but not all, I guess. What happens is the router intercepts and redirects requests for routerlogin.net to the internal router admin site. It's a trick to help router owners who would have trouble with the question "what is the IP address of your router?". Unfortunately, there are lot of things that can go wrong with this, always better to use the actual IP address of the router.