How do we know the required parameters of hook's callback method?
I've never had to use this specific hook before, but I have found a breakdown of the callback in the Drupal docs:

https://api.drupal.org/api/drupal/modules!filter!filter.api.php/function/callback_filter_process/7

Pretty sure everything you're after will be described in the documentation. You can view all the other Filter API functions within the documentation here:

https://api.drupal.org/api/drupal/modules!filter!filter.api.php/7