To answer your specific questions...

Backups are always a good idea before any upgrade or patch, but in this case they will not be required as a part of the process, only if the process fails at some point.

The Unity server will have to restart as a part of the patch process, so all services will restart as a part of that.

Yes, the way upgrades and patches work with the Cisco Linux platform is that the upgrade/patch installs to the inactive parttion.  This way you can install the upgrade while the server is functioning.  However, either when the installation is finished, or at a later time to coincide with a maintenance window, you must switch active and inactive partitions to put the new version into service.  This does involve a reboot.

As for a CUCM is concerned, the ports will go out of service and then come back into service.  Nothing should need to be done.  However, you will need to test that.  I have seen voicemail ports that need to be reset from the CUCM side in order to function after an upgrade or an install.

Chris