Lukas,
Their shouldn’t be anything blocking WooCommerce Ajax in the Free version. If you are using the Pro version and have the Plugin Firewall, the solution is below. I suspect that the issue with Ajax might be your caching plugins. Which plugin are you using for caching??
http://forum.ait-pro.com/forums/topic/woocommerce/
/woocommerce/assets/js/(.*).js