How to shorten code with function?

You can make your own function to minimize the characters typed for each time you want to repeat the call to get_posts:

in functions.php (perhaps):

function print_piwa($postcount=2, $cat_id=81) {
    ?>
    <div class="wiadPodtyt">
        <ul>
            <?php 
            $piwa = get_posts(array(
                'posts_per_page' => $postcount,
                'cat' => $cat_id,
                'post__not_in' => $news_ids,
                'offset' => 1
            ));
            foreach ($piwa as $post) {
                setup_postdata($post);
                ?>
                <li>
                    <a href="https://wordpress.stackexchange.com/questions/73204/<?php the_permalink(); ?>" class="subtytulyWiad">
                        <?php the_title(); ?>
                    </a>
                </li>
                <?php
            }
            ?>
        </ul>
    </div>
    <?php
}

You’ll obviously need to figure out what variables you want to set and use them accordingly, but there’s no reason you can’t use get_posts in a function of your own making.

Then you can just call your function in your templates:

<?php print_piwa(5, 81); ?>