function wpa_alter_cat_links( $termlink, $term, $taxonomy ){
    if( 'category' != $taxonomy ) return $termlink;

    return str_replace( '/category', '', $termlink );
}
add_filter( 'term_link', 'wpa_alter_cat_links', 10, 3 );

function wpa_alter_cat_links( $termlink, $term, $taxonomy ){
    if( 'category' == $taxonomy && 0 == $term->parent ){
        return str_replace( '/category', '', $termlink );
    }
    return $termlink;
}
add_filter( 'term_link', 'wpa_alter_cat_links', 10, 3 );

RedirectMatch 301 ^/category/(.*)$ /$1

function loadPageFirst() {
    // get the actual category
    $actualCategory = get_category (get_query_var('cat'));
    // get the page with the same slug
    $matchingPage = get_page_by_path($actualCategory->slug);

    // If no match, load the normal listing template and exit (edit if you are using a custom listing template, eg. category.php)
    if (!$matchingPage) {
        include( get_template_directory() . '/archive.php');
        die();
    }

    // Make a new query with the page's ID and load the page template
    query_posts('page_id='.$matchingPage->ID);
    include( get_template_directory() . '/page.php');
}

add_filter( 'category_template', 'loadPageFirst' );