Add post-thumbnail after first paragraph including the caption

Something like this should work

add_filter( 'the_content', 'insert_featured_image', 20 );

function insert_featured_image( $content ) {
  global $post;

  if ( has_post_thumbnail($post->ID) ) {
    $thumbnail_caption = get_the_post_thumbnail_caption( $post );

    if ( $thumbnail_caption )
        $caption = '<span class="image-caption">' . $thumbnail_caption . '</span>';
    else 
        $caption = ''; // You can set this to whatever you want. 

    $img = '<p>' . get_the_post_thumbnail( $post->ID, 'full' ) . '</p>';
    $content = preg_replace( '#(<p>.*?</p>)#', '$1' . $img . $caption, $content, 1);
  }

  return $content;
}