You can use sockets to send either a GET or POST query to your web server (which is what it looks like you are already doing). You should be able to receive data from this query. It would require using RCON on the server to be able to have an event on the website send unsolicited data to the server.
I wrote a function a long time ago to send ban information to a webpage that I wrote using POST. I've attached it here for reference. It doesn't retrieve any data back from the server but I didn't need to for this application.