Featured post in current category page by specific tag

untested – try to add the current category into the query:

$args = array(
        'category__in' => array(get_query_var('cat')),
        'posts_per_page' => 1,
        'tag' => 'featured',
    );

http://codex.wordpress.org/Class_Reference/WP_Query#Category_Parameters

what should I add to not duplicate the featured post with posts the loop below the featured section?

check:
http://codex.wordpress.org/The_Loop#Multiple_Loops_in_Action
particular the section after the headline ‘Note for Multiple Posts in the First Category’
i.e. using an array for $do_not_duplicate and the 'post__not_in' parameter in a query for the rest of the posts.

example – assuming that you have the post ID of the ‘featured’ post in the $do_not_duplicate array;

global $wp_query;
$args = array_merge( $wp_query->query, array( 'post__not_in' => $do_not_duplicate ) );
query_posts( $args );

http://codex.wordpress.org/Function_Reference/query_posts#Preserving_Existing_Query_Parameters

you could also paste the full code of your category archive template (into a pastebin …) and someone might have a look at your code.