Hello,

1) I have created a test product and set the sale price and the badge is shown just fine.

URL for the test product: https://gioiellipreziosi.eu/uncategorized/test

As you are using a third party plugin “Acowebs Woocommerce Dynamic Pricing” and you want the code for sale price in the single product page in the backend. I saw your screenshots, its requires customization and this is beyond our limitations and support policy.

You need to contact the plugin author.

2) I have test both the pages, Wishlist and Compare and both were working just fine and shown the products when I add a product to wishlist or for compare.

Video for clarification: https://jmp.sh/EVTjaNL

Kindly check back after clearing your site and browser cache.

3) If you want to hide the categories section from the product page shown in the below screenshot then used the below CSS code in theme settings >> custom CSS >> global Custom CSS:

Screenshot: https://jmp.sh/6B51ENA

.single-product-page .product_meta .posted_in{
display:none;
}

Best Regards.