[Support request] I can’t translate my site via .po and .mo

Hi,
I’m using a multisite with multilingualpress. I’m trying to translate one or two words in a theme, but I’m failing.The theme is Blankslate (https://it.wordpress.org/themes/blankslate/). It’s a blank theme which I personalized a lot via child theme (in themes/blankslate-child).
This is the head of the style.css

/*
Theme Name:   Child di BlankSlate.
Description:  mio
Text Domain:  blankslate-child
Domain Path: /languages
Author URI:  https://www.lgwebdesign.it
Template:  blankslate
Version:  1.1
License:  GNU General Public License v2 or later
License URI: https://www.gnu.org/licenses/gpl-2.0.html                 
*/

I’m trying to translate the file archive-product.php, regarding WooCommerce. The files is inside /wp-content/themes/blankslate-child/woocommerce
I’m trying to modify this page https://chiaragini.it/negozio/, specifically translate in Italian the “category” and “products” titles.

<?php
/**
 * The Template for displaying product archives, including the main shop page which is a post type archive
 *
 * This template can be overridden by copying it to yourtheme/woocommerce/archive-product.php.
 *
 * HOWEVER, on occasion WooCommerce will need to update template files and you
 * (the theme developer) will need to copy the new files to your theme to
 * maintain compatibility. We try to do this as little as possible, but it does
 * happen. When this occurs the version of the template file will be bumped and
 * the readme will list any important changes.
 *
 * u/see https://docs.woocommerce.com/document/template-structure/
 * u/package WooCommerce\Templates
 * u/version 3.4.0
 */

defined( 'ABSPATH' ) || exit;

get_header( 'shop' );

/**
 * Hook: woocommerce_before_main_content.
 *
 * u/hooked woocommerce_output_content_wrapper - 10 (outputs opening divs for the content)
 * u/hooked woocommerce_breadcrumb - 20
 * u/hooked WC_Structured_Data::generate_website_data() - 30
 */
do_action( 'woocommerce_before_main_content' );

?>
<header class="woocommerce-products-header">
	<?php if ( apply_filters( 'woocommerce_show_page_title', true ) ) : ?>
		<h1 class="woocommerce-products-header__title page-title"><?php woocommerce_page_title(); ?></h1>
	<?php endif; ?>

	<?php
	/**
	 * Hook: woocommerce_archive_description.
	 *
	 * u/hooked woocommerce_taxonomy_archive_description - 10
	 * u/hooked woocommerce_product_archive_description - 10
	 */
	do_action( 'woocommerce_archive_description' );
	?>
</header>
<?php

$x = woocommerce_maybe_show_product_subcategories();
$y = __('Category', 'blankslate-child');
//$y = 'Categorie';
    //seguono nostre categorie
    if(strlen(trim($x)) != 0)
    echo "<h2>{$y}</h2><ul class=\"products columns-4\">{$x}</ul>";
    //fine categorie
?>
<h2 id="h2prodotti"><? _e('Products', 'blankslate-child') ?></h2>
<?php
if ( woocommerce_product_loop() ) {
	/**
	 * Hook: woocommerce_before_shop_loop.
	 *
	 * u/hooked woocommerce_output_all_notices - 10
	 * u/hooked woocommerce_result_count - 20
	 * u/hooked woocommerce_catalog_ordering - 30
	 */
    do_action( 'woocommerce_before_shop_loop' );
    remove_filter( 'woocommerce_product_loop_start','woocommerce_maybe_show_product_subcategories' );
	woocommerce_product_loop_start();
	if ( wc_get_loop_prop( 'total' ) ) {
		while ( have_posts() ) {
			the_post();

			/**
			 * Hook: woocommerce_shop_loop.
			 */
			do_action( 'woocommerce_shop_loop' );
			wc_get_template_part( 'content', 'product' );
		}
	}
	woocommerce_product_loop_end();

	/**
	 * Hook: woocommerce_after_shop_loop.
	 *
	 * u/hooked woocommerce_pagination - 10
	 */
	do_action( 'woocommerce_after_shop_loop' );
} else {
	/**
	 * Hook: woocommerce_no_products_found.
	 *
	 * u/hooked wc_no_products_found - 10
	 */
	do_action( 'woocommerce_no_products_found' );
}

/**
 * Hook: woocommerce_after_main_content.
 *
 * u/hooked woocommerce_output_content_wrapper_end - 10 (outputs closing divs for the content)
 */
do_action( 'woocommerce_after_main_content' );

/**
 * Hook: woocommerce_sidebar.
 *
 * u/hooked woocommerce_get_sidebar - 10
 */
do_action( 'woocommerce_sidebar' );

get_footer( 'shop' );

This is my child theme functions.php

<?php
function mytheme_add_woocommerce_support() {
	add_theme_support( 'woocommerce' );
}
add_action( 'after_setup_theme', 'mytheme_add_woocommerce_support' );

// supporto multilingua
function child_theme_slug_setup() {
    load_child_theme_textdomain( 'parent-theme-slug', get_stylesheet_directory() . '/languages' );
}
add_action( 'after_setup_theme', 'child_theme_slug_setup' );

//add_action( 'after_setup_theme', 'blankslate_child_setup' );
//function blankslate_child_setup(){
	
//	$x = load_child_theme_textdomain('blankslate', get_stylesheet_directory(). '/languages');
// }
/* fine commento codice Gigli */
/*
function debug_textdomain(){
	//$locale = apply_filters( 'theme_locale', determine_locale(), $domain );
	
	//$locale = get_locale();
    //$locale_file = get_template_directory() . "/languages/$locale.php";
	//echo "<br>";
	//echo $locale;
	//echo "-";
	//echo $locale_file;
}
add_action('load_textdomain','debug_textdomain');
*/
// menus
function register_my_menus() {
  register_nav_menus(
    array(
      'menu-lingue' => __( 'Menu lingue' )
     )
   );
 }
 add_action( 'init', 'register_my_menus' );

// deregister contact form 7
add_action( 'wp_print_styles', 'wps_deregister_styles', 100 );
function wps_deregister_styles() {
    wp_deregister_style( 'contact-form-7' );
}

?>

This is the main theme functions.php

<?php
add_action( 'after_setup_theme', 'blankslate_setup' );
function blankslate_setup() {
load_theme_textdomain( 'blankslate', get_template_directory() . '/languages' );
add_theme_support( 'title-tag' );
add_theme_support( 'automatic-feed-links' );
add_theme_support( 'post-thumbnails' );
add_theme_support( 'html5', array( 'search-form' ) );
global $content_width;
if ( ! isset( $content_width ) ) { $content_width = 1920; }
register_nav_menus( array( 'main-menu' => esc_html__( 'Main Menu', 'blankslate' ) ) );
}
add_action( 'wp_enqueue_scripts', 'blankslate_load_scripts' );
function blankslate_load_scripts() {
wp_enqueue_style( 'blankslate-style', get_stylesheet_uri() );
wp_enqueue_script( 'jquery' );
}
add_action( 'wp_footer', 'blankslate_footer_scripts' );
function blankslate_footer_scripts() {
?>
<script>
jQuery(document).ready(function ($) {
var deviceAgent = navigator.userAgent.toLowerCase();
if (deviceAgent.match(/(iphone|ipod|ipad)/)) {
$("html").addClass("ios");
$("html").addClass("mobile");
}
if (navigator.userAgent.search("MSIE") >= 0) {
$("html").addClass("ie");
}
else if (navigator.userAgent.search("Chrome") >= 0) {
$("html").addClass("chrome");
}
else if (navigator.userAgent.search("Firefox") >= 0) {
$("html").addClass("firefox");
}
else if (navigator.userAgent.search("Safari") >= 0 && navigator.userAgent.search("Chrome") < 0) {
$("html").addClass("safari");
}
else if (navigator.userAgent.search("Opera") >= 0) {
$("html").addClass("opera");
}
});
</script>
<?php
}
add_filter( 'document_title_separator', 'blankslate_document_title_separator' );
function blankslate_document_title_separator( $sep ) {
$sep = '|';
return $sep;
}
add_filter( 'the_title', 'blankslate_title' );
function blankslate_title( $title ) {
if ( $title == '' ) {
return '...';
} else {
return $title;
}
}
add_filter( 'the_content_more_link', 'blankslate_read_more_link' );
function blankslate_read_more_link() {
if ( ! is_admin() ) {
return ' <a href="' . esc_url( get_permalink() ) . '" class="more-link">...</a>';
}
}
add_filter( 'excerpt_more', 'blankslate_excerpt_read_more_link' );
function blankslate_excerpt_read_more_link( $more ) {
if ( ! is_admin() ) {
global $post;
return ' <a href="' . esc_url( get_permalink( $post->ID ) ) . '" class="more-link">...</a>';
}
}
add_filter( 'intermediate_image_sizes_advanced', 'blankslate_image_insert_override' );
function blankslate_image_insert_override( $sizes ) {
unset( $sizes['medium_large'] );
return $sizes;
}
add_action( 'widgets_init', 'blankslate_widgets_init' );
function blankslate_widgets_init() {
register_sidebar( array(
'name' => esc_html__( 'Sidebar Widget Area', 'blankslate' ),
'id' => 'primary-widget-area',
'before_widget' => '<li id="%1$s" class="widget-container %2$s">',
'after_widget' => '</li>',
'before_title' => '<h3 class="widget-title">',
'after_title' => '</h3>',
) );
}
add_action( 'wp_head', 'blankslate_pingback_header' );
function blankslate_pingback_header() {
if ( is_singular() && pings_open() ) {
printf( '<link rel="pingback" href="%s" />' . "\n", esc_url( get_bloginfo( 'pingback_url' ) ) );
}
}
add_action( 'comment_form_before', 'blankslate_enqueue_comment_reply_script' );
function blankslate_enqueue_comment_reply_script() {
if ( get_option( 'thread_comments' ) ) {
wp_enqueue_script( 'comment-reply' );
}
}
function blankslate_custom_pings( $comment ) {
?>
<li <?php comment_class(); ?> id="li-comment-<?php comment_ID(); ?>"><?php echo comment_author_link(); ?></li>
<?php
}
add_filter( 'get_comments_number', 'blankslate_comment_count', 0 );
function blankslate_comment_count( $count ) {
if ( ! is_admin() ) {
global $id;
$get_comments = get_comments( 'status=approve&post_id=' . $id );
$comments_by_type = separate_comments( $get_comments );
return count( $comments_by_type['comment'] );
} else {
return $count;
}
}

I used poedit to create .po and .mo, but the translation is not applied. Any clues?