The exim logs are /var/log/exim_*. You'll want to sift through /var/log/exim_mainlog* and /var/log/exim_rejectlog*

There are many functions in Cpanel Dedicated Server which can be managed through ssh.

When cPanel & WHM is installed, a number of predefined scripts become available in your server’s /usr/local/cpanel/scripts directory. You can use any of the scripts simply by typing its location in a terminal session. For example, if you wanted to run the update script, you would type:

• /usr/local/cpanel/scripts/upcp
  

Here is a list of links which I have come across recently to secure cpanel servers.

From the Official Documentation

• http://www.cpanel.net/2007/06/10-tips-for-making-your-cpanel-and-whm-servers-more-secure.html
• http://docs.cpanel.net/twiki/bin/view/AllDocumentation/WHMDocs/SecureServerChecklists