How to allow a user with some role to let people to register their new accounts in drupal 7?
In Drupal 7 you can use Administer Users by Role module


  Administer Users by Role : This module allows site builders to set up fine-grained permissions for allowing users to edit and delete other users — more specific than Drupal Core's all-or-nothing 'administer users' permission. It also provides and enforces a 'create users' permission.


Reference:


Create role for changing user accounts and not admins