Hi Wolf,
I would help if I could, but from what you say your server is in "safe mode", which I understand does not allow Moodle to do things it must do - such as read and write to files and folders elsewhere in the file hierarchy.
At least I am pretty sure that you won't be able to complete the automatic installation of Moodle until you switch off Safe Mode. To switch off Safe Mode, you need to change a setting in "php.ini" (the PHP settings file) and then restart your web server. If you are using a shared server, you may not have sufficient privileges to be able to do this yourself, so please consult with your ISP helpdesk.
If I were in your situation, I would bypass the install script and create the config.php by hand. It is not difficult, and only requires inserting a handful a values, so that Moodle knows how to access to DB and how to access its files on the server and via the web. Have a look at config-dist.php in your Moodle directory.
If you still get the basedir error having created your own config.php, then I would try one final thing, and that is to try to add the inaccessible folder to the list of accessible folders.
- in the "basedir" error message, you will see the "include" list of directories, which the folders on your server that PHP is allowed to access. Probably this list finishes with "/tmp". Let's say it is "/path/to/www:/tmp" Copy the list of "include" folders in your message
- now, look for a file called ".htaccess" in your Moodle folder. If there is not there, create it (as a text file)
- open the ".htaccess" file with a text editor
- copy and paste the following text to ".htaccess"
<Directory /path/to/www/moodle/>
php_admin_value open_basedir "/path/to/www:/path/to/moodledata:/tmp"
</Directory>
- save the modified ".htaccess"
- access Moodle again
But I feel you would do best to devote your energies to getting Safe Mode switched off
all the best
Gordon