These are all warning about PHP not being able to load an extension.
SourceGuardian
http://www.sourceguardian.com/
magickwand
http://www.magickwand.org/
This module enables PHP access to the ImageMagick MagickWand API
which appears to be an interface related to the last:
imagick
http://www.imagemagick.org/script/index.php
For Moodle, related to manipulation of images, only php-gd is required (from what I re-call).
If your server was standalone CentOS, the extensions (initialization files) located in /etc/php.d/ are auto loaded.
Check your php info page in Moodle. It discloses the location of php extensions your install will attempt to load. Section entitled: Additional .ini files parsed
To the best of my knowledge, none of the above should/would affect backups of Moodle courses.
But, they do need attention.
Module compiled with module API=20060613
PHP compiled with module API=20090626
Indicates when PHP was compiled ... reference to the mod had a 20090626 but the module installed compiled with 20060613
When php is upgraded, php extensions must also be upgraded.
Since you are remotely hosted, this is an area (install of not only version of PHP but extensions as well) to which you don't have access so this is all on the hosting providers end. Surprised your hosting provider is no help on that!
Wonder if your php has php-zip extension loaded?
http://docs.moodle.org/24/en/admin/environment/php_extension/zip
'The native PHP zip extension is required to let Moodle 2 read or write ZIP compressed archives.' ... which what a .mbz is.
'spirit of sharing', Ken