Hello wat,
I am sorry for the delay of this reply, I have been debugging your site / server for almost 10 hours now
Okay, you can actually disregard those messages you see in the "System Info" in your Joomla back end because, if they are going through the Joomla's API which is JFile and JFolder, they should be safe with suExec.
The reason why you are seeing those directories as "not writable" is because Joomla is using is_writable method in PHP to check if those folders are writable but because is_writable is a php function, it is returning false because php scripts are running as the user "apache".
To really solve your permission issues, on the server there's 2 choice:
1. This is more ideal and everything should be 755 NOT 777. However, php scripts on the site need to explicitly use JFile and JFolder from Joomla and not rely on built-in php functions to store files. I am not too sure which extension should fail but if you hit errors, you should notify the developer.
2. This is a much quicker way around, is to have every file / folders to be owned by apache / apache and do not use suExec. This way, existing scripts will most likely work fine but I am not sure about Directadmin though.
By the way, I have also migrated the items over to EasySocial now