Odd / Even posts add class minus first post

You can do this in multiple ways, but you will need something commom to all posts, exemple:

<div class="post"></div>
<div class="post"></div>
<div class="post"></div>
<div class="post"></div>
<div class="post"></div>

then in your css:

.post:not(:first-child) {
  // add the rules of the class you wanted to add
}

Just select all elements except the first-child of posts with the class post and add the rules of the class you wanted to add.

You also can do with js/jquery:

$('.post:not(:first-child)').addClass('myclass');

It’s the same logic as with css, but if you wnat to add a separate class you can do it.

or you can do with php:

<?php $count = 0 ?>
<?php while ($homenews_query -> have_posts()) : $homenews_query -> the_post(); ?>

<?php if ($count != 0): ?>
  <!-- stuff here -->
<?php endif ?>

<?php if ($homenews_query->current_post % 2 == 0): ?>
  <!-- stuff here -->
<?php else: ?>
  <!-- stuff here -->    
<?php endif ?>

<?php 
  $count++;
  endwhile;
  wp_reset_postdata();
?>

I know that the first post, is the one in the index 0 so a just check if the count is != 0.

or simpler, you have an attribute called current_post just check if you’re not in the first post, like this:

<?php while ($homenews_query -> have_posts()) : $homenews_query -> the_post(); ?>

<?php if ($homenews_query->current_post != 0): ?>
  <!-- stuff here -->
<?php endif ?>

<?php if ($homenews_query->current_post % 2 == 0): ?>
  <!-- stuff here -->
<?php else: ?>
  <!-- stuff here -->    
<?php endif ?>
<?php 
  endwhile;
  wp_reset_postdata();
?>

Edit: I posted with the inverse logic, fixed now.