Setting field not saving on front-end

Make the $options variable global by changing the header_add_content() function to the following:

function header_add_content() {
    global $options; 
    $options = get_option('header_options');
}
add_filter("the_content", "header_add_content");

Then declare $options as the global $options on the front-end template before you use it, for example:

<p><?php global $options; echo $options['txt_mail']; ?></p>