Why my meta boxes won't show in front post page?

Assuming that your site front page is displaying a static page, the reason that your meta data doesn’t appear on the site front page is because you only enable your post custom meta box for post post-types:

$meta_box = array(
    // ...
    // refer to this array key
    'page' => 'post',
    // ...
);

// ...

function mytheme_add_box() {
    global $meta_box;

    add_meta_box( 
        $meta_box['id'], 
        $meta_box['title'], 
        'mytheme_show_box', 
        // Refer to this parameter, which tells
        // WordPress that this meta box applies
        // to the post post-type
        $meta_box['page'], 
        $meta_box['context'], 
        $meta_box['priority']);
}

// ...

// Refer to this hook, that tells WordPress
// to hook your save post meta callback into
// the save action for the post post-type
add_action('save_post', 'mytheme_save_data');

To use this same post custom meta also on the page post-type, you’ll need to call add_meta_box() for both post and page, and you’ll need to hook your save post meta callback into both save_post and save_page. (Note: you’ll also want to hook into draft_post and draft_page to spare yourself headaches caused by auto-saves.

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