A fixed version of this plugin: https://wordpress.org/plugins/rss-via-shortcode-on-page-post/

rss-via-shortcode.php

<?php
/*
Plugin Name: RSS Via Shortcode for Page & Post
Version: 1.2.b
Plugin URI: http://susantaslab.com/
Description: Makes it easy to display an RSS feed on a page
Author: Susanta K Beura
Author URI: http://susantaslab.com/
License: GPL v2
Usages: [rssonpage rss="Feed URL" feeds="Number of Items" excerpt="true/false" target="_blank|_self"]
*/

function SLB_rss_sc( $atts ) {
	extract(shortcode_atts(array(
	   	"rss" 		=> '',
		"feeds" 	=> '10',
		"excerpt" 	=> true,
		"target"	=> '_blank'
	), $atts));

	if ( $rss != "" && $rssFeed = get_rss_feed( $rss ) ) {

		$rssFeed->enable_order_by_date(false);
		$maxitems = $rssFeed->get_item_quantity( $feeds );
		if ($maxitems == 0)
			return '<ul><li>Content not available at'.$rss .'.</li></ul>';

		$rss_items = $rssFeed->get_items( 0, $maxitems );

		$content = '<ul>';

		foreach ( $rss_items as $item ) {
			$content .= '<li>';
			if ($target != '_self'){
				$content .= '<h3><a href="';
				$content .= trim($item->get_permalink());
				$content .= '" target="';
				$content .= $target;
				$content .= '" rel="external">';
				$content .=  $item->get_title();
				$content .= '</a></h3>';
			}
			else {
				$content .= '<h3><a href="';
				$content .= trim($item->get_permalink());
				$content .= '" rel="external">';
				$content .= $item->get_title();
				$content .= '</a></h3>';
			}
			if ( $excerpt != false && $excerpt != "false") {
				$content .= '<br/><span class="rss_excerpt">';
				$content .= $item->get_description();
				$content .= '</span>';
			}
			$content .= '</li>';
		}
		$content .= '</ul>';
	}
	return $content;

}

add_shortcode( 'rssonpage', 'SLB_rss_sc' );

function Custom_Plugin_Links( $links, $file ) {

   if ( strpos( $file, 'rss-via-shortcode.php' ) !== false ) {
      $new_links = array(
               '<a href="http://wordpress.org/support/view/plugin-reviews/rss-via-shortcode-on-page-post?rate=5#postform" target="_blank">' . __( 'Rate us' ) . '</a>',
               '<a href="http://support.susantaslab.com/" target="_blank">' . __( 'Contact support' ) . '</a>',
               '<a href="http://susantaslab.com/career/freelance-job-openings/" target="_blank">'.__('Demo: Job Feed').'</a>',
               '<a href="http://susantaslab.com/blog/bestsellers-at-amazon/" target="_blank">'.__('Demo: Amazon Bestsellers').'</a> ',
               '<a href="http://susantaslab.com/blog/hot-trends-at-ebay/" target="_blank">'.__('Demo: eBay Products').'</a>'
            );

      $links = array_merge( $links, $new_links );
   }

   return $links;
}

add_filter( 'plugin_row_meta', 'Custom_Plugin_Links', 10, 2 );

if (!function_exists('get_rss_feed')){
	function get_rss_feed( $url ) {
		require_once( ABSPATH . WPINC . '/class-feed.php' );

		$feed = new SimplePie();

		$feed->set_sanitize_class( 'WP_SimplePie_Sanitize_KSES' );
		$feed->sanitize = new WP_SimplePie_Sanitize_KSES();
		$feed->set_useragent('Mozilla/5.0 (Windows NT 6.1) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/37.0.2062.120 Safari/537.36');

		$feed->set_cache_class( 'WP_Feed_Cache' );
		//$feed->set_file_class( 'WP_SimplePie_File' );

		$feed->set_feed_url( $url );
		$feed->set_cache_duration( apply_filters( 'wp_feed_cache_transient_lifetime', 12 * HOUR_IN_SECONDS, $url ) );
		do_action_ref_array( 'wp_feed_options', array( &$feed, $url ) );
		$feed->init();
		$feed->handle_content_type();

		if ( $feed->error() )
			return new WP_Error( 'simplepie-error', $feed->error() );
		return $feed;
	}
}

?>

Caching is the culprit. Slightly modifying the feed URL (ie: adding a slash at the end) will usually fix this.

Code above doesn't make use of the SimplePie method set_file_class, which gives the best results, but may also impede caching.

Hey, did you ever manage to also get the image from each external post? Thanks!