To use first image rather than featured image you can replace :
if ( has_post_thumbnail() ) {
$large_image_url = wp_get_attachment_image_src( get_post_thumbnail_id(), 'large');
echo '<a href="' . $large_image_url[0] . '" class="thumbnail cboxElement" title="' . the_title_attribute('echo=0') . '" >';
the_post_thumbnail( 'eo-featurette',array('class' => 'featurette-image img-responsive') );
echo '</a>';?>
<?php }
to
if (preg_match_all('/<img.+src=[\'"]([^\'"]+)[\'"].*>/i', $post->post_content, $matches)) {
//check if an image exists at all
$first_thumb = $matches [1] [0];
// replace the thumbnail size part to get large image url
$source_img_rep = preg_replace('/(-\d+x\d+)?\.(\w{3,4})$/','',$first_thumb);
$ext = pathinfo($first_thumb, PATHINFO_EXTENSION);
$first_source = $source_img_rep . '.' . $ext;
echo '<a href="' . $first_source . '" class="thumbnail cboxElement" title="' . the_title_attribute('echo=0') . '" ><img class="img-reponsive" src="'.$first_thumb.'" alt="' . the_title_attribute('echo=0') . '" /></a>';
}
else if ( has_post_thumbnail() ) {
$large_image_url = wp_get_attachment_image_src( get_post_thumbnail_id(), 'large');
echo '<a href="' . $large_image_url[0] . '" class="thumbnail cboxElement" title="' . the_title_attribute('echo=0') . '" >';
the_post_thumbnail( 'eo-featurette',array('class' => 'featurette-image img-responsive') );
echo '</a>';?>
<?php }
Remember to use a child theme. Don’t know what you are looking for in terms of width or height of the carousel, but the carousel is going to get a rework in the next version(bootstrap carousel will be replaced with owlcarousel). Let me know if you’ve further questions, marking as resolved.