Just updated Events Maker to 1.1.2 and now I can't add locations and categories.

Sounds like a Javascript error. Did you update any other plugins too?

I understand. But we did not change anything in thise admin pages. Can you provide a temporary admin access?

Ok, at least those 2 scripts are unnecessary in event categories admin page:

<script type='text/javascript' src='http://71.18.82.125/thc2/wp-content/plugins/wc-shortcodes/includes/js/admin.js?ver=1.39'></script>
<script type='text/javascript' src='http://71.18.82.125/thc2/wp-content/themes/spa/js/kaya_admin_custommeta.js?ver=3.8.1'></script>

But there’s more:
The POST request (create new category) that is handled by admin-ajax.php returns this: 500 Internal Server Error

I wonder what it really points to in your case – .htaccess? permalinks? There must be something wrong with your install / config.

Start with the code/plugins I posted above, then check everything again.