SmarterMail offers Inbound Messages and Outbound Messages reports at the domain level -- they're not in one report, but you can get user traffic, inbound and outbound, from those reports. By default, they display Trend data, but if you change the report's Mode you can get user detail. You can even see individual users in their own report by selecting a user from the Users dropdown. 

SmarterMail uses a flat file system, not a database, so storing detailed info at the level requested in the second and third bullets, then extracting it, would be a pretty big hit to disk space, not to mention processing that data. It may be possible script something that would extract that info from Delivery logs. 

For the last bullet, I guess a bit more info on what they mean by "review complete activity". 

I hope that helps a little bit. 

Also, this sounds similar to this other post: https://portal.smartertools.com/community/a97548/feature-request-comprehensive-mailbox-audit-log-with-search-table-view-and-self-service-capabilities.aspx

I have Python scripts, called from Declude, that implement my filtering architecture and store email metadata in a SQL database.    From SQL, the reporting options are endless, but I roll my own I. SQL Management Studio.  If you are willing to do some development effort to adapt it to your needs and provide a web interface, I am sure that it could create whatever they want and package as part of your brand identity.   Code available on request.  Just send a PM.