How can I give the permission to edit, update, or delete a comment or a user profile to specific roles? I am using the ACL module for Drupal 7 to give the permission to edit, update, and delete nodes to specific users. It works perfectly.
I want the same feature for comments and user profiles.
Is there any specific module or API for the same?
There's the Comment Permissions module:


  The Comment Permissions module enables control of commenting by user role and by node type. Additional user permissions for selected node types are added to the user access system so you can configure commenting with more control than Drupal core provides.


It does have a (dev) Drupal 7 release, it's just not listed on the module page for whatever reason. You can find the archive here.

It will need testing before you can use it in a production site, but it's a very small module and a cursory glance at the code suggests it should work. I used that code as the base for a more advanced comment permissions module (including soft-deleting etc) some time back and don't remember finding any problems with it.