How to Add Thumbnail to "entry-header" div class

Is this done in the loop-blog.php?

It depends on when your thumbnail should appear. The loop-blog.php is used when showing the “posts page” (multiple posts) while the loop-single.php is used for single pages.

I’m struggling with the sample code.

What sample code?

On both loop-blog.php and loop-single.php the header text is added immediately after the opening <article> tag. You might want to add your image there.

I’d like to point out that this functionality is not really specific to my themes and is more about modifying core WP functions. You may get better luck asking on forums like these:
https://wordpress.org/support/forum/themes-and-templates
https://wordpress.org/support/forum/plugins-and-hacks

For the “custom field” part, there’s already a plugin that could handle that:
https://wordpress.org/plugins/advanced-custom-fields/

For joining the content of the custom field to the post title, you could use the title filter. This is just a sample/pseudo code to show how it could be done.

add_filter( 'the_title', 'ra_custom_post_title' );

function ra_custom_post_title( $title ) {

   $custom_field = get_post_meta($post_id, $key, $single);

   if ( ! empty($custom_field) ) {
      $title = $custom_field . $title;
   }

   return $title;
}

Read more on https://codex.wordpress.org/Custom_Fields