How will you create a custom menu that would go to the house page however the url isn't static? Like I'm inside a test server at this time, therefore the url is localhost/mywordpress. I put a '/' within the url for my custom menu however it redirects to localhost.

It is possible to method to place it in ways it may would go to the home page of my test server?

Thanks

Only use /wordpress/ and don't forget to alter it back around the production server.

Even better, use Apache VirtualHosts to map an imitation domain to some document root. Take a look at my answer on setting up a VirtualHost.