You can try something like:
if ( is_category() ) {
$cat = get_category( get_query_var( 'cat' ) );
// $cat_id = $cat->cat_ID;
$cat_name = $cat->name;
// $cat_slug = $cat->slug;
$args = array(
'category_name' => $cat_name,
'post_type' => 'post',
'orderby' => 'menu_order',
'order' => 'DESC',
);
...
The function you are looking for is get_category, as well as is_category to check that the query is for an existing category archive page.