drupalchat module is it free or not ?

Reading the project's homepage, it becomes clear that the module is free - as is every module that you download from the drupal.org website.

However, to use it, the module has to connect to a chat service, and the module is designed to integrate with the services of node.js for that.

node.js runs its own http service, and has to be customised to listen to particular ports etc. For this reason, most shared hosts don't run, or allow you to run, node.js. You'd have to find a shared host that explicitly supports it (and there are a few - but none that I've used). If you're running Drupal on a VPS or dedicated server, there's nothing stopping you from installing and configuring node.js yourself. Or: You can use a commercial node.js service, such as the one linked from the project homepage. In that case, you'd be paying for the node.js service - but the module itself is still free.

Note that drupalchat works without nodejs. So you can install it and use it for free on your site (works ok in a shared hosting environment) it just won't scale very well with a large amount of simultaneous users. After about 5-10 users it begins to lag. This is where nodejs comes in. It will allow you to scale up. Also note that the maintainers provide a testing nodejs server for free. Just follow the project page to set up.