Ryuhei Yokokawa

Plugin will allow you to fetch the WP-API (WP-JSON-API) call with a “lang” variable. It will retrieve the right content from WPML/WP.
This only works with WPML and WP-API installed. I tested only with the latest version as of now: 
* WPML 3.1.9.6 
* WP REST API 1.2.1

WPML to WP API

Allows you to request a language with your WP-API and WPML site.

digitalissimo

If you need to get the information from another site or your site using JSON API (https://wordpress.org/plugins/json-api/) you can use this plugin. 
For slideshow this plugin use Cycle2 (http://jquery.malsup.com/cycle2).
<h4>Shortcode</h4>
<pre><code>[getapi url="www.mysite.com" limit="5" type="[CYCLE or LIST]"]:
</code></pre>
<ul>
<li>
url: url before ?json=get_recent_posts
</li>
<li>
limit: number element of json result
</li>
<li>
type: “Cycle” is a slideshow of thumbs or “List” is the list of post titles
</li>
</ul>

Get Json Api

Retrieve the results of the API of a site that uses the plugin JSON API

WPML to WP API vs Get Json Api