Registered users and Unregistered visitors can submit support tickets. To allow unregistered visitors (users who are not logged in) to submit a ticket, you must enable this setting in BILLETS >> Configuration. [Billets automatically creates an account for new unregistered users when they submit a ticket - to allow you to create an on-going support relationship with that user and track all their issues.]
You can set-up 'managers' for ticket categories.
Anyone who has been set-up as a manager can respond to tickets on the front-end of your site (if you create the appropriate manager link). And they will only be able to manage the categories to which you assign them as managers.
Users who have access to the admin-side of your site can also manage tickets.
Billets will send an email notice to whichever managers you assign to a category. The emails are taken from the Joomla entry for the manager. If a user is assigned as a manger for a category, they will get email updates whenever a new ticket (or comment on a ticket) is added.
Tickets which are not assigned to a category when they are created will NOT generate an email notice to managers.