Install process removes permission
The initial server error reads like this:
You don't have permission to access /typo3/sysext/install/Start/Install.php on this server.
The permission to the document root folder is modified and thus TYPO3 is currently locking out itself during the install process.
Looks like $GLOBALS['TYPO3_CONF_VARS']['BE']['folderCreateMask'] is used as targetPermission...
So, either leave out the root node or find a way to determine the correct permission.
In my case I get a
Permission denied: /.../introduction/.htaccess pcfg_openfile: unable to check htaccess file, ensure it is readable, referer: http://.../typo3/sysext/install/Start/Install.php