Sorry for this newbie question. Can node.js run in any hosting provider like Fastdomain? We have an account in fastdomain where we upload our Website made in PHP. I allowed SSH in our host and tried installing node.js but it didn't work. I've been searching the internet but there is no exact answer to this.
No, you can not run Node.js on every hosting provider. You need certain base capabilities. If your hosting provider doesn't directly support Node.js (like Heroku does), then you need to be able to shell into your server. You also need access to a C compiler to build Node.js or the ability to install packages for your system.
Once you get Node.js installed then you need root access to be able to run it on port 80. You can get around this if your provider provides reverse proxy service.
The fact that you can shell in is a good start. It might be possible on Fastdomain, but to be sure you should contact Fastdomain support. Every hosting provider is different and if you have shared hosting then the answer is most likely no. You generally need dedicated hosting to run Node.js.