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It depends on your definition of "non Joomla! files".

If this means files inside the same directory as your Joomla! site, then yes they will be included as long as they are not inside the cache, tmp, logs or backup output directories.

If this means files outside your Joomla! directory (e.g. one level above) then no, they will not be backed up unless you explicitly tell Akeeba Backup to do so using the Off-site Directories Inclusion feature.

If this means database tables inside the same database as Joomla! - database, not database server, there's a huge difference ;) - then, yes, the tables will be backed up automatically unless you tell Akeeba Backup to do otherwise.

If this means database tables inside a different database than the one used by Joomla! then no, nothing will be backed up unless you use the Extra Databases Inclusion feature.

In other words, if it's inside Joomla!'s directories or database -even if it is not part of your Joomla! site- it will be backed up. Otherwise, you have to tell Akeeba Backup what you want to be backed up. Just think about it. How would Akeeba Backup -a component running inside Joomla!- know about what runs outside of Joomla! and how to back it up unless you tell it?

So, what do you define as "non Joomla! files"?

Yes, you would need the off-site directories inclusion. Just note that all off-site files are transferred in a new directory named external_files, placed inside your transferred site's directory. This is done on purpose, since you give Akeeba Backup FTP access to the Joomla! site's directory, which doesn't always guarantee access to one directory above.

Just go to Components, Akeeba Backup and click on the Off-Site Directories Inclusion button (you must have Akeeba Backup Professional installed). Consult this documentation page for more information. It also answers your other question.