the admin gets the email twice, because you have marked for the admin to get a notification and you probably have inserted the admin email as the email to send the responses as well (two emails are sent).
If you have a token based research, then you need to do what Shnoulle said, if it is not token based, you need to include a question with the email address of the participant. Then you need to include the response to that email into the field for the email where the responses should be sent to. Search a little in the forum, this was discussed before. I think you should find this also in the limesurvey manual.