Hello,
“New” label is not set automatically, you can configure it manually. From editing products and by setting the sale price.
Screenshot for Clarification: https://ibb.co/wNKhJFF
“Hot” products marked as “Featured” will have a badge with “Hot” label. To add the hot label you need to mark the product as featured from Products.
Screenshot for Clarification: https://ibb.co/bH6sNhG
If you are trying to ask anything else then provide with some relevant screenshots to check it myself and help you out accordingly.
Best Regards.