.mainHeader h1 { padding: 20px 0; }
This will reduce the space around the logo.
If you want to move the related items, you have to edit the item.php file located at html/com_k2/default/item.php.
Locate the <div class="itemRelated"> element.
These are the related items, you need to move the entire <div> (be careful where it closes around line 705 and also include the if, endif statements).
Once you 've copied you need to paste the code above the item navigation (<div class="itemNavigation">).
Now for the logo. This can only be done by pushing the social buttons to the bottom.
Locate the following block of code in index.php
<?php if(count($social)): ?>
<div class="column small-12 large-6 textRight socialMenu">
<ul>
<?php foreach($social as $provider): ?>
<li>
<a class="linkIs-<?php echo $provider->class; ?>" target="_blank" href="<?php echo $provider->url; ?>">
<span><?php echo $provider->name; ?></span>
</a>
</li>
<?php endforeach; ?>
</ul>
</div>
<?php endif; ?>
<div class="clr"></div>
<!-- Logo -->
<h1 id="logo" class="column">
<a href="<?php echo $siteurl; ?>">
<?php if($this->params->get('siteLogo')): ?>
<img src="<?php echo $this->params->get('siteLogo'); ?>" alt="<?php echo $this->params->get('siteLogoAltText', $sitename); ?>" />
<?php else: ?>
<span><?php echo $this->params->get('siteTextAsLogo', $sitename); ?></span>
<?php endif; ?>
</a>
</h1>
And replace it with
<div class="column small-12 large-6 textRight socialMenu"
<!-- Logo -->
<h1 id="logo" class="column">
<a href="<?php echo $siteurl; ?>">
<?php if($this->params->get('siteLogo')): ?>
<img src="<?php echo $this->params->get('siteLogo'); ?>" alt="<?php echo $this->params->get('siteLogoAltText', $sitename); ?>" />
<?php else: ?>
<span><?php echo $this->params->get('siteTextAsLogo', $sitename); ?></span>
<?php endif; ?>
</a>
</h1>
</div>
<div class="clr"></div>
<?php if(count($social)): ?>
<div class="column small-12 textCenter socialMenu">
<ul>
<?php foreach($social as $provider): ?>
<li>
<a class="linkIs-<?php echo $provider->class; ?>" target="_blank" href="<?php echo $provider->url; ?>">
<span><?php echo $provider->name; ?></span>
</a>
</li>
<?php endforeach; ?>
</ul>
</div>
<?php endif; ?>
<div class="clr"></div>
PS. Always backup before doing any edits and always keep a copy of these backed up files.