How to rewrite url wordpress?

You should hook add_rewrite_rule() into init

Assuming http://local/rieltplus/ is your homepage, and category/catalog/ is a category archives, this should work:

add_action('init', function() {
    add_rewrite_rule(
        'category/catalog/([^/]+)?$',
        'index.php?category_name=catalog&type=$matches[1]&price_min=1000&price_max=2000&area_min=5&area_max=50&room_num=5&etage=2&plan=old',
        'top'
    );
});

If you want to make that available to any category then mention it in the comments.

By the way, local/rieltplus/category/catalog/TYPE&price_min is not a valid URL, unlike local/rieltplus/category/catalog/TYPE?price_min or local/rieltplus/category/catalog/TYPE/?price_min..

To get the type variable, use get_query_var( 'type' ) but first add it to the main query:

add_filter('query_vars', function($vars) {
    $vars[] = "type";
    return $vars;
});

You should flush the permalink structure by saving your permalink structure in the settings > permalinks screen or using flush_rewrite_rules() ONLY ONCE.

Edit – As per your other question in the comments

add_action('wp', function() { // this will work as long as GET type is the first is the query string
    if( "catalog" === get_query_var( "category_name" ) && isset( $_GET["type"] ) ) {
        if( ! empty( $_GET["type"] ) ) {
            $type = strval( $_GET["type"] );
            $url = $_SERVER["REQUEST_URI"];
            $url = str_replace( array( "?type={$type}&", "?type={$type}" ), "{$type}?", $url );
            $url = str_replace( "?&", '?', $url );
            wp_redirect( $url );
            exit;
        }
    }
});