Hi,
This popup is from the legacy add to cart system, not the new add to cart system. The image and the message would come out like you want if you turned off the add to cart legacy setting of the HikaShop configuration.
The cross button is actually added to the message of the old popup system by your template, so it would require CSS change to the template to remove it, and the product image would be quite hard to add to the old popup system, although, a developer could probably work out some code to do it in the file "notice" of the view "checkout".