I'm running a real time web application which uses Symfony 2 PHP framework on the backend. I want to implement websockets for my real time interaction. Is it possible to install a node.js server on the same machine as my Symfony 2 server to handle websocket connections? If so, is it standard to open another port (say 81) to handle the websocket connection?
Yes, it is possible. Why not? It's just another application.
As for the second question. You can either open another port, which is easy to handle (WebSockets are not limited with cross-origin policy) but you may lose some data (cookies) or you can put a proxy which will send HTTP requests to web server and WS requests to Node.JS server. The latter can be recognized by having special header Upgrade: websocket. Either way WebSocket server has to listen on different port (unless you are developing application entirely in Node.JS).