A: To exclude a specific product from showing up in recommendations universally on the whole site an exclusion can be made for the specific product. See the documentation for Applying exclusions for more details on this interface.
When configuring a widget if a category of items should be excluded from recommendations, such as excluding all warranties, then a rule excluding a certain category of product can be configured. See the Defining product recommendation rules documentation for more information on how this can be performed.
If there are a large number of categories that need to be excluded from all recommendations that is easily defined it is recommended to reach out to your customer success manager to see if the analytics team for personalization can configure a back end rule that would prevent certain products from being recommended.