Will address the last question first ...
*IF* there is a chance you will go into production with Moodle, why not start with a LTS version even if running in a private network? There is enough difference between Fedora and CentOS that would/will facilitate moving to production quickly cause you've tackled the issues with CentOS already. Production becomes 'childs play', so to speak.
Permissions are now too liberal and ill advised. Unless you saw a log that said 'permission denied' - which you haven't yet, cause not looking in the right place! Now the task is to revert those very liberal and potentially dangerous permissions on /var ... plus the subdirectories.
On a CentOS boxen (similar to Fedora) here's what you just opened to the globe:
[root@sos var]# ls
account cvs ftp lib log nfs preserve run tmp yp
cache db games local mail nis racoon spool tux
crash empty gdm lock net-snmp opt rails streaming www
nfs, for example should have nobody, gdm should have root:gdm, cups should have root:lp, streaming should have drwx------, etc. and so forth. Box shouldn't ever be accessible to outside world and probably need not be used even on a private network ... unless you plan on making it a 'honey pot' ... cause that's what it is now.
The directory that one should have focused upon was 'www'. Inspection of the config file for apache ... /etc/httpd/conf/httpd.conf would have given you clues as to where to concentrate your efforts in resolution of the problem.
Log for apache ... all are notices ... not errors.
The log to check ... is the apache *error* log - which is probably in /var/log/httpd/ ... error_log
If PHP configured to log errors, there could be a php_error.log in /var/log/
I sometimes install and use a text based browser on the server:
yum -y install lynx
After installation, from command line:
lynx http://192.168.40.251/ to test. It will show errors not seen via browser.
MySQL/MariaDB running? Has login password set? Has a database been created for moodle - character set utf8 collate utf8_general_ci?
ps aux |grep mysqld
PHP has all that it needs?
php -m (shows mods for php loaded)
Blank screens indicate issues ... obviously ... clear workstation cookies and history to site. Clear/purge caches of Moodle (php /pathtomoodlecode/admin/cli/purge_caches.php
Before making the next attempt, turn on debugging via config.php file.
Lines in config-dist.php file to place into config.php
// Force a debugging mode regardless the settings in the site administration
// @error_reporting(E_ALL | E_STRICT); // NOT FOR PRODUCTION SERVERS!
// @ini_set('display_errors', '1'); // NOT FOR PRODUCTION SERVERS!
// $CFG->debug = (E_ALL | E_STRICT); // === DEBUG_DEVELOPER - NOT FOR PRODUCTION SERVERS!
// $CFG->debugdisplay = 1; // NOT FOR PRODUCTION SERVERS!
un-commented of course.
And after resolution of problems, advise leaving the lines in config.php and commenting them out again.
So ... how about we stop now .... and see what we get.
'spirit of sharing', Ken