Hello,
If you do not want to display the discount label then edit your products and remove the sale price.
Screenshot for clarification: https://jmp.sh/O1hwKY3
To edit the discount label you can use the below CSS code in global custom CSS area under theme settings >> custom CSS:
body .product-labels .onsale {
background-color: red;
width: 70px;
height: 70px;
}
You can change the sorting order of products from Appearance >> Customize >> WooCommerce >> Product Catalog >> Default product sorting.
To change the sorting order of products which shown inside the product tabs in your home page, you need to edit the product tab theme element one by one and from the “Data Settings” tab you will see the option of “Order by”, you can change the order from this option and save the changes.
Screenshot for your satisfaction; https://jmp.sh/5VQm5U3
If you want to hide the sold out items you can check the option “Out of stock visibility” from WooCommerce >> Settings >> Products >> Inventory. This option will hide out of stock items from the catalog.
Best Regards.