Please go to your preferences page and make sure your "See Mature Topics" setting is set. Setting it to "Yes" means you see the Mature Topics forum (contains political and religious debates). Setting it to "No" means you do not see those threads.
Go to your PM box and scroll all the way down. At the bottom, on the right, you'll find this function:
Just download your PMs to your local computer and then delete them to make room for more. Doesn't take more than a minute, and you won't lose anything because you can still look at your old PMs on your very own PC!