I have 2 problems.
In categories field in foreign language the data is shown only for 16 letters. This is both in the site and in the admin section. English characters are OK.
In the database in the localhost server this section is shown in incomprehensive characters - so called monkeys.
The collation is utf8_general_ci, following the icouto's advices. Editing query_factory.php file did not worked for me, so I left it in original state.