Hello,
I saw the screenshot you attached.
1) You need to create different attributes for the products from Products >> Attributes.
Screenshot for Clarification: https://ibb.co/x2MwJqg
Then you need to assign items to the attribute and then use them as variations from edit products.
Then the drop-down will be visible for the products you used the attribute as variations.
You can find more instructions about the attributes and variations in the following link:
https://docs.woocommerce.com/document/variable-product/
https://docs.woocommerce.com/document/managing-product-taxonomies/
2) I have visited your website and the icons are working fine on my end. Please clear cache and check back.
Screenshot for Clarification: https://ibb.co/T4bGLw6
Best Regards.