Warning: Cannot modify header information – headers already sent

First of all, you misunderstood “How do I solve the Headers already sent warning problem?”

As you said, you’ve changed:

function mhm_footerheader_position ()

to:

function mhm_footerheader_position()

The only difference I see is the space between mhm_footerheader_position and (). The whitespace problem in header already sent error, isn’t about the space between function_name and (). It’s about space that gets into the output before any HTTP header is sent.

Secondly, you don’t want to output anything in widgets_init action, this the the wrong place for any output. The error you are getting is because you are giving output in widgets_init action and in wp-login.php HTTP header is being sent after this action hook.

I can’t say exactly where you want to output the footer-header widget area, it depends on your theme. However, the following CODE will output it in the footer and solve your Error:

    function mhm_footerheader_position () {
        echo '<div id="footer-header"><div class="wrap">';
        genesis_widget_area('footer-header');
        echo '</div></div>';
    }

    add_action ('wp_footer','mhm_footerheader_position');

You may read this to understand the Hearer Already Send Error better.