I noticed that MySQL is not running as mysqld_safe on my server. Is that normal?
If your server runs an RHEL 6 based operating system, yes, it can run as mysqld_safe. Otherwise, it is normal to not have mysqld_safe running.
As described in the MySQL documentation, mysqld_safe "is the recommended way to start a MySQL server on Unix;" however, on systems using systemd (This is a technical term used for a sub-system of RHEL/CentOS 7+), mysqld_safe is not installed nor used because it is not needed.
In fact, if MariaDB ends up getting started as mysqld_safe via race condition or manually, the cPanel & WHM software will report it as down. For more information on this, take a look at the following article: