How can I structure my pseudo footer nav code with wordpress codex code?

I tested this as a function. You can place it in your footer or functions.php theme file and call it in your themes footer section. See the comments for links to the functions used.

function wpse_101774_footer() {

    // Start this part of footer on new line.
    echo "\n";

    foreach ( array( 14, 19 ) as $page_id ) {

        // Start .footercat div.
        echo "<div class="footercat">\n";

        // Print the Parent post anchor markup.
        // See: http://codex.wordpress.org/Function_Reference/get_permalink
        // See: http://codex.wordpress.org/Function_Reference/get_the_title
        printf( '<h2><a href="https://wordpress.stackexchange.com/questions/101774/%s">%s</a></h2>', get_permalink( $page_id ), get_the_title( $page_id ) );

        echo '<ul>';

        // List the child pages.
        // See: http://codex.wordpress.org/Function_Reference/wp_list_pages
        wp_list_pages( array(
            'depth'       => 1,
            'child_of'    => $page_id,
            'post_type'   => 'page',
            'post_status' => 'publish',
            'title_li'    => '',
        ) );
        echo '</ul>';

        // End .footercat div.
        echo "\n</div><!-- end .footercat -->\n";
    }

    $blog_post_id = 3081;

    // Print the Blog page anchor markup.
    // See: http://codex.wordpress.org/Function_Reference/get_permalink
    // See: http://codex.wordpress.org/Function_Reference/get_the_title
    printf( '<h2><a href="https://wordpress.stackexchange.com/questions/101774/%s">%s</a></h2>', get_permalink( $blog_post_id ), get_the_title( $blog_post_id ) );

    // Start .footercat div.
    echo "<div class="footercat">\n";

    echo '<ul>';

    // Add comma separated list of ctegory IDs in place of "1" (For example, 1, 45, 6 ).
    foreach ( array( 1 ) as $category_id ) {

        // Get the category object for this category ID.
        // See: http://codex.wordpress.org/Function_Reference/get_category
        $category = get_category( $category_id );

        // Get this category's posts.
        // See: http://codex.wordpress.org/Function_Reference/get_posts
        $posts = get_posts( array(
            'posts_per_page'  => 5,
            'category'        => $category_id,
            'post_type'       => 'post',
            'post_status'     => 'publish',
            'suppress_filters' => true
        ) );

        $post_anchors="";
        if ( $posts ) {
            $post_anchors="<ul>";
            foreach ( $posts as $post ) {

                // Print this category's posts.
                // See: http://codex.wordpress.org/Function_Reference/get_permalink
                // See: http://codex.wordpress.org/Function_Reference/get_the_title
                $post_anchors .= sprintf(
                    '<li><a href="https://wordpress.stackexchange.com/questions/101774/%s">%s</a></li>',
                    get_permalink( $post->ID ),
                    get_the_title( $post->ID )
                );
            }
            $post_anchors .= '</ul>';
        }

        // Print this category's anchor and post anchors, if any.
        // See: http://codex.wordpress.org/Function_Reference/get_category_link
        printf( '<li><a href="https://wordpress.stackexchange.com/questions/101774/%s">%s</a>%s</li>', get_category_link( $category_id ), $category->name, $post_anchors );

    }
    echo '</ul>';

    // End .footercat div.
    echo "\n</div><!-- end .footercat -->\n";
}