It's a little more complicated
You have in fact three different items here.
1) The DNS name/IP address and port number to pass to TCP Open Connection.
2) The DNS name/IP address and port number from the webserver you want to get the info from
3) The path on that server
Without proxy server you use the DSN name and port number of the web server you want to get the data from to pass to TCP Open connection.
And the GET request line only contains the path on that server to the resource you want to receive.
With proxy you pass the DNS name and port number of the proxy to the TCP Open Connection function.
The GET request now contains the entire URL with webserver and path to the resource.
There is an example for a little VI library here that contains a subVI that seperates the various parts from the two input informations of the proxy server address (no proxy if empty) and the actual URL request address.
Authentification is an entirely different beast. It's also added to the HTTP Header as extra lines, but Basic authentication, while easy to implement is really a joke as it offers no security at all but rather gives the wrong sense that it is secure, and the more advanced authentications are a bit more involved to implement.
