Translate arguments of a user added custom code [closed]

Because you are hardcoding the link, you will need to use icl_link_to_element() function and wrap any text you want to translate inside a gettext function:

<?php icl_link_to_element( 'ID_of_your_news_page', 'page', '<h4>' . __('News') . '</h4>' ); ?>

This way you will get the correct version of the link based on the current language with the text translated. If you want translate the slug you have to do it in the page/post edit screen.

After you have edited the code in your question, I think it is better to use get_permalink() and icl_object_id(). As I said before, you should wrap any text in your theme inside a gettext function in order to be translatable. For the href value, first you have to create the two versions of the news page and translate the slug for the two versions (/news/ and /новости/) and then:

<a href="https://wordpress.stackexchange.com/questions/138339/<?php echo get_permalink( icl_object_id( ID_of_news_page,"page', true, ICL_LANGUAGE_CODE) ); ?>" class="hover-on">

  <div class="hoverdiv-feat hide-for-small">
        <img src="location" class="attachment-portfolio-feat wp-post-image" alt="uudised"></div>    
   <div class="overlay hover-on">

     <h4><?php _e('News'); ?></h4>

   </div><!-- END .overlay -->      
    <div class="no-hoverdiv-feat show-for-small">
        <img width="299" height="227" src="location" class="attachment-portfolio-feat wp-post-image" alt="uudised"></div>

</a>

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