How to configure the Answers module to organize questions by product subpages?
I'm assuming you're using the most recent 7.x.-4.x version of the Answers module. The new demo site uses a further enhanced version of the most recent dev release. For example the views have been enhanced and will be pushed to D.O shortly. These views are available already in Views Export format via files attached to comment #5 in issue #2783513).

Here is a screenprint of the (new) view to show all the questions:



Note the Topics column in the above views result: it's just a term reference field, added as an extra field to the "Question" content type (which comes with the module). With that in mind, you could use a similar approach:


Step 1: Add a similar (mandatory) field, I'd recommend an Entity reference field. So that when a question is created the question author indicates which product your question is about.
Step 2: Enhance the view to add a filter related to the product.
Step 3: Adapt the path of your enhanced view that matches your requirements.


Note: regarding the "...so that they can only see..."-part of your question it may be sufficient to just filter the view as described above. But if you actually want to restrict access to any of the questions, you can use the access method/module of your choice to limit access to the Question nodes. Red flag: be aware of the "Disable Query Rewriting" discussion (and tune that views setting if needed).

Disclosure: I'm a co-maintainer of this module.