Some updates about my investigation.
1. For me problem occures in FF 21 and 20.
2. Problem doesn't exist in Opera (and Chrome as I wrote before).
3. When I send string to an active element it will appear in address bar not on page. It should appear on input element that gets focus through js.
4. The problem exists for PHP and Python using RemoteDriver. So it's not related with PHP.
5. Problem doesn't exist for Selenium RC but this could be expected.
I'll try to check under ubuntu because maybe window manager or operating system matter.
Best regards,
piotrr