I am not using a shortcode, when I do, the text of the shortcode is displaying instead of the accordion. Or do I do something wrong?

You have to use shortcode to make it work. I have used WordPress shortcode on my test site as shown in the attached screenshot and it is not displaying as text which means it is working.

Please test the same gallery shortcode on your site and if it works then it means the shortcodes are working in the description but not the shortcode provided by woocommerce addons so contact the woocommerce addons creators regarding this.

Still having troubles with woocommerce too, to see a product you have to be logged in and I still didn’t find out why

Please make sure the visibility of product is public and not private as shown in the second attached screenshot.