Is there an XML Web Service that can get posts, categories and other data from the site?

WordPress ships with an XML-RPC interface that’s enabled by default. It gives you the ability to both retrieve and edit/create content on the site via XML.

There’s quite a bit of detail about the API available on the Codex.

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Updated

There aren’t (to my knowledge) any existing systems in place that do XML over GET for WordPress. Webpages tend to be some form of (X)HTML already and, if following the XHTML spec closely, your theme alone might produce something parse-able.

However, that’s not the only option in place.

If you take a look at some of the newer AMP work being done with WordPress, you’ll see how developers are leveraging custom URL rewrite endpoints to serve different content for the same resource. For example:

• http://yoursite.com/2016/09/cool-post-bro – Delivers standard HTML
• http://yoursite.com/2016/09/cool-post-bro/amp – Delivers AMP markup

You could use the same pattern to code an /xml rewrite endpoint that presents your post in whatever arbitrary markup as you need.

To get you started …

Enable an endpoint

function xml_init() {
    add_rewrite_endpoint( 'xml', EP_PERMALINK );
}
add_action( 'init', 'xml_init' );

Intercept requests so you can prepare XML

function xml_maybe_change_markup() {
    if ( ! is_singular() || is_feed() ) return;

    // Only intercept the right requests
    if ( false === get_query_var( 'xml', false ) ) return;

    add_action( 'template_redirect', 'xml_render' );
}
add_action( 'wp', 'xml_maybe_change_markup' );

Actually render XML

function xml_render() {
    $post_id = get_queried_object_id();

    // Get the post, build your XML document, print it to the page

    exit;
}

As I don’t know what exact output you need, I leave building the XML document as an exercise for you 🙂