Here are the ones I use myself: http://mirrors.n-ix.net/mariadb/mariadb-10.0.13/yum/

Well, that's your app's problem. Apparently there's a version mismatch between your Ruby libs and MySQL server libs.

Status code is being output on stderr, while actual JSON code is on stdout. You can do following:

ajenti-ipc v export Website > website.json

You need to use an absolute path to the file.

Please check your NGINX error log under /var/log/nginx/website.error.log

Do file permissions on them allow reading for www-data user?

Yes, looks good.

You can remove the "subdomain" PMA site

You only need one website (because it will be working at a single domain).

You can remove the "subdomain" PMA site, as you won't be using it. You need to re-create your PMA content config under the "main" website now, while using a "/phpmyadmin" URL pattern.
You can just follow our phpMyAdmin tutorial, but use the new URL pattern. Also, you'll need to point custom path of the new content entry to PMA installation.

Yes, just add your phpMA content entries to the main website and use "/phpMyAdmin" URL pattern. You might also need to also add some custom configuration to deal with PHP redirects