How to create a email notification to subscribers and the author who posted a comment programmatically in drupal 7?
I do not see a way to allow users to subscribe to comment notification, is that your issue?

In case it is you might have to do something like
Create a menu item as 'Subscribe to comments' check this link to ajaxify for menu item. On page callback of your custom menu subscribe the current user(global $user) to the comments, to hold the data you can simply use a custom table let's name as mymoudle_comment_subscription with columns as record_id|uid|comments_on_type|flag update this table in the subscription menu callback,

Rest is what you have covered in your code, i.e. implement hook_comment_update to notify on existing comment update, hook_comment_delete notify user on comment delete, hook_comment_insert notify user on new comment is added. In your hook Implementation query your custom table 'mymoudle_comment_subscription' fetch all uids get user mail by uids or in case you do not allow user to change emails you can store email directly in your custom table and use drupal_mail as your code shows to mail all users.