I think you might get docManager to run if you edit line 8 of this file:
/var/www/html/site/core/components/docmanager/controllers/index.php
Change the require_once call to include the full, actual path of the docmanager.class.php file.
require_once 'absolute/path/to/docmanager.class.php';
If you change the log_deprecated System Setting, the other two messages should go away.