In your example, $posts_page
contains the ID of the page for posts, you can use that with any API function that accepts a post ID.
For the featured image:
$posts_page = get_option( 'page_for_posts' );
$post_thumbnail_id = get_post_thumbnail_id( $posts_page );
$url = wp_get_attachment_image_src( $post_thumbnail_id, 'your-custom-size' );
echo $url;
And outputting post title with filters applied:
$posts_page = get_option( 'page_for_posts' );
$title = get_post_field( 'post_title', $posts_page );
if ( ! is_wp_error( $title ) ) {
echo $title;
}