I don't want to publish my domain, that's why I use mysite.com
Wordpress site is not mine.
As I mentioned above:
... when I succeeded to generate
www.mysite.com/%D0%92%D1%80%D1%8A%D0%B7%D0%BA%D0%B8/
it opens successfully also as
www.mysite.com/Връзки/
So, I guess my provider is OK with the cyrillic letters.
I think that I won't use Artio for this moment. First, because generating of cyrillic letters in URLs is not so important for SEO. And second, because Artio generates duplicate content in the Joomla path menu - mysite.com/index.php and mysite.com