Multiple images per post – Show random image elsewhere

I’d like to be able to choose one of those 6 images that I’d like to display as a large image within the same template file.

This would probably fit as the Post Thumbnail/Post Featured Image.

Additionally, out of these 6 images I’d like to randomly call in 1 random one on to a custom page template in another loop elsewhere on the site.

Try using get_children() with the 'orderby' => 'rand' and 'numberposts' => 1 parameters.

Assuming you know how to get the ID of the post whose image attachments you want to display, as $post_id:

$random_post_images = get_children( array(
    'post_parent'    => $post_id,
    'post_mime_type' => 'image',
    'post_type'      => 'attachment'
    'orderby'        => 'rand',
    'numberposts'    => 1,
) );

This will return an array of one image, as an object:

$random_post_image_object = $random_post_images[0];

Now, you can output the image, using wp_get_attachment_image():

$random_post_image = wp_get_attachment_image( $random_post_image_object->ID, 'thumbnail' );