How to trigger an action when a site receives an email?
Here is how you might get it to work:


Use Mailhandler to create nodes by eMail. The content of the node could be the actual content of the request as contained in the eMail.
Use Rules to react to the event "after saving content" and combine it with the Message module to send the eMail back to the user.


If you're not familiar (enough/yet) with Rules, checkout the 32 (!!!) great, and free, video tutorials Learn the Rules framework, organized in 7 chapters. For more details about the Message module, refer to some interesting Use Cases detailed within its Community Documentation.