How do I create anonymous emails sent by users and allow other users to reply back to the anonymous email?
You could use the following components:


an email server you control to create temporary email accounts, or a mail relay service.
use Relation or a custom user field for a user's anonymous email thru user02193213@yoursite.com. Enforce uniqueness of this field. Relation can do alot of this for you as a developer (create a user &lt;-&gt; anonymous email relation, attach category tags to the Relation Entity itself and use relation_query to build reusable lookup functions.
store a mapping of Drupal uid to anonymous emails. In general this is outlined here: https://stackoverflow.com/questions/8179047/email-piping-in-php-like-craigslist-how-do-i-associate-real-emails
upon content submission use Rules to lookup anonymous email addresses of content owner to logged in user and send the email. Your email server you control can then forward to real addresses.


Questions regarding email setup are not drupal setup and inappropriate here. I've just outlined an approach for the Drupal side of things.