The item.php needs the code to be like

<?php echo JHTML::_('date', $this->item->created , JText::_('K2_DATE_FORMAT_LC2')); ?>

Yea but how can I change that?

And what could be the reason that I can't publish comments that where entered? I can edit them but not publish. I have set it on no automated publishing

You have to create K2 template overrides, like you did with the module, read here getk2.org/documentation/tutorials/174-templating-with-k2-and-the-concepts-of-sub-templates on how you can do so and then edit item.php and add the two definitions for your date's format in the item page as well.

For the publishing of comments, what joomla! and K2 version do you use?

I did the overrides as you told me but it still doens't work.

I use Joomla v3.2.1 and K2 v2.6.7

Is a link to your page available to check it out?

Also try to upgrade your K2 to the 2.6.8 SVN version which is compatible with 3.2.1 joomla! and fixes some issues.
Download it here: getk2.org/assets/get/

Don't forget to get a backup of your site first.