3-column layout with categories

What theme are you using?

If you are comfortable programming in PHP you could use WP_Query to create you own queries.

Those if conditions must be inside the loop.

Assign all posts of a category to an array and after the loop ends (endwhile), display them as you like.

I have made a sample index.php file, you can expand on that – https://gist.github.com/jesinwp/76248ebd827e26ab74e6

To have multiple categories in a single column use

if ( in_category( array( 'category2', 'category3' ) ) )

The advanced custom fields code you posted isn’t formatted properly, please place them inside backticks or paste them on pastebin.com and share its URL.

The get_field() and the_field() functions need the $post_id argument when used outside the loop.

<?php if ( get_field( 'url2', $post['the_ID'] ) ) { ?>
   <a class="button" href="<?php the_field( 'url2', $post['the_ID'] ) ?>" target="_blank"><?php the_field( 'beschriftung_url2', $post['the_ID'] ) ?></a>
<?php } ?>

http://www.advancedcustomfields.com/resources/get_field/

For this to work the post ID must be assigned to the array inside the loop

if ( in_category( 'category1' ) ) {
    $cat1[ $i ]['the_ID'] = get_the_ID();