/var should have 755 permissions. It was worth changing it to 777 as you did as a test. But for system security you should revert back to the original /var permissions i.e. chmod 755. /tmp IMO is fine as you have it. Although more conservative folk might suggest 755 there as well.

/usr/share/doc/rtorrent/examples/rtorrent.rc is unlikely to be the active rtorrent config file. This is a reference copy. The active .rtorrent.rc config file should be in your home directory. The leading period signifies that it is a system (hidden) file, so you need to use ls -a or ls -h to see it. In rare instances the config file may be on a custom path.. Check screen, init or cron for clues, if you have reason to suspect that.

$ ps aux | grep rtorrent

ps aux lists the active processes on your machine. You are looking to see what the active web server is and if screen has any anomalies
In your list, screen rtorrent isn't specifying a custom path.. so most likely you will find another .rtorrent.rc file in your home directory. Cron is running, it's a bit of a long shot, but I would see how your cron jobs are configured. And apache appears to be your web server. So see if you can pull up the apache config info with..

$ httpd -V

httpd_root will tell you where apache is installed. And httpd_root will tell you where the httpd.conf file is located. Concatenate the two to derive the full path. Or alternately, do a brute force search with find or locate..

$ find / -name 'httpd.conf' -print
$ locate httpd.conf