With get_posts()
, try using the category ID instead of the category slug.
For example:
// Carousel articles
$args = array( 'numberposts' => 3, 'orderby' => 'date', 'category' => 1 );
$carousel = get_posts($args);
// News articles
$args = array( 'numberposts' => 3, 'orderby' => 'date', 'category' => 2 );
$news = get_posts($args);
// Featured articles - max 2 posts
$args = array( 'numberposts' => 2, 'orderby' => 'date', 'category' => 3 );
$featured_posts = get_posts($args);