Convert attachment ID into url?

You need the function wp_get_attachment_image_src() see http://codex.wordpress.org/Function_Reference/wp_get_attachment_image_src

In your code it would be something like:

<?php foreach(get_field('connections') as $relationship): ?>
    <?php $img = wp_get_attachment_image_src( get_post_meta($relationship->ID, 'company_logo', true ), 'thumbnail' ); ?>
    <img src="https://wordpress.stackexchange.com/questions/40232/<?php echo $img[0]; ?>"  width="<?php echo $image_attributes[1]; ?>" height="<?php echo $image_attributes[2]; ?>" />        
    <a href="<?php echo get_permalink($relationship->ID); ?>"><?php echo get_the_title($relationship->ID) ?></a>
    <br />
<?php endforeach; ?>

You can change ‘thumbnail’ to your desired size.