Custom Taxonomy Archives Page Errors

The problem is this:

register_taxonomy('author', 'post', array( //tax args here... ));

The first argument, which is taxonomy name, you’ve set to author. WordPress uses that value as the taxonomy query var if a value isn’t explicitly declared. When this taxonomy is queried, author is used to pass the requested term slug to the query.

The problem with that is that WordPress already uses author to query for users via their ID. Visiting those term pages results in WordPress trying to query for posts where user ID is 0, which will always be a 404 (any non-numeric string is interpreted as invalid and becomes integer 0).

Either change the name to something else:

register_taxonomy('something_unique', 'post', array( //tax args here... ));

Or, explicitly set query_var to something other than author.

register_taxonomy('author', 'post', array(
    'query_var' => 'something_unique',
    // the rest of your tax args...
));