Which hook will load after node page load and file download
It's not really clear what you need re node hooks, since your title says "after node page load" and the body of your question says "after a node is loaded". Those are very much two different things. If you're looking for a hook that fires after the page has been displayed on the front end, there isn't one (though you could theoretically implement your own using AJAX). 

Your best bet would be to consult the list of Node API Hooks and select the one that best suits your exact use case.

To get notified of file downloads through the private file system you can implement hook_file_download(). There's nothing similar for public file downloads, as Drupal's default behaviour is to pass straight through to existing files, without bootstrapping (hence no hook could ever be fired).