Hmmm I have never heard of open_basedir restriction before. I did a quick google search and see that it is a PHP ini option (http://php.net/manual/en/ini.core.php). Here is a quote from another page:
PHP open_basedir protection tweak is a Safe Mode security measure that prevents users from opening files or scripts located outside of their home directory with PHP, unless the folder has specifically excluded.
It seems you will have to disable open_basedir or include the directories that Geeklog needs to access that are outside of the web root.
With mb_strlen you need the PHP mbstring extension loaded.
One of the Geeklog Core Developers.