When a request is raised on behalf of an existing customer, there isn't any way to identify that the request has been raised that way. It just looks as if the customer him/herself raised it.
Have a custom field, or an automated comment that helps to inform the customer that the request was being raised on behalf of him or her.
None. The agent raising the request could add a comment to the ticket to mention that its being raised on behalf of the user, but that's a manual way of doing things and not very easy to track.