A router is usually platform agnostic
Not sure what a "Windows web site" is but almost all routers have a built in web page interface that can be accessed, on a Mac, by using Safari or Firefox.
The url used depends on the make of the router, in your case the url is 192.168.0.1 on the Winstar Router
I assume that you are able to access the Router and view the configuration. Is that correct?
Again, is there security on the wireless network? If there is, turn it off and see if you can connect then.
Again, what Router are you currently trying to use?
Your niece's name and password has nothing to do with connectivity but probably a lot to do with accessing her Belkin Router.