Fatal error: Uncaught exception 'Exception' with message 'Could not connect to database: Connection refused'
Headshaker's response is 100% correct. This definitely and unequivocally means that MySQL is not running or is (for some other reason) not accepting connections.
No matter how many times you restart Centova Cast it's not going to fix this because this has nothing to do with Centova Cast; the problem is with MySQL.
Starting Centova Cast: cc-control Invalid option: -F
Usage: /usr/local/centovacast/sbin/cc-control [options]
This is a different and completely unrelated issue; it seems you have somehow done a partial upgrade to 3.0.6. (Maybe the upgrade failed halfway through? Perhaps it failed *because* of the MySQL problem above?)
In any case, you need to get MySQL running again (and to be clear: you MUST get MySQL running FIRST), and then run /usr/local/centovacast/sbin/update again to finish upgrading Centova Cast.