Help required to fix resource issues on Linode VPS

On our Linode VPS, we have a LAMP setup (The Linux is CentOS 6.x). There are multiple sites on our server hosted which we have done by using Apache’s virtual hosting. Issue #1: The Linode frequently shuts itself down occasionally or some sites stop working every other day, we believe because of the high CPU usage-which we get warning messages from quite often (and we usually reboot the server or Linode to solve the problem). There are only two sites on the server which are currently being used and both don’t have upto a hundred users/visits per day. So its clearly not because of the large number of users. We would require help with fine tuning to avoid this. Some cron jobs had been identified by a previous system admin to be responsible but those have been stopped. We would also want to verify that they are not running and causing this issue. Issue #2: Linode support has told us that it takes 4 hours for our automatic backups to complete and they think it would have an effect if we would try to restore from backups at a later date. They have pointed to a mail folder which they think is a catch all mailbox. We suspect that it might also be causing some of the other problems we have been experiencing. We would need help with looking into this with the view of emptying the mailbox if it is indeed a catch all mailbox. The emails for all the sites are handled via Dovecot, MySQL, Postfixadmin and Postfix configuration. I can share the discussion with Linode support on this issue via Freelancer.com’s Private Message if you request to see the chain of discussion on this issue to further understand it. The budget for this project is about $60. We would be more favourably disposed to lower bids from Sys Admins with proven track records here on Freelancer.com.