The short answer is "No".

This question has 3 parts:

1. Can the API list questions and answers about a product?
   Yes, if they are tagged and/or use keywords (like product numbers) that the API can search on.

2. Can the API be use to ask new questions?
   No. Officially, the API currently (version 2.1) does not support posting new questions or answers. This may change in the future, as alpha-stage API products appear to have write capability.

3. Are there any Stack Exchange sites that allow this?

4. I can't see any of the current Stack Exchange sites being very friendly to this kind of question. I imagine they'd get flagged and closed a lot.
   (They used to be considered "too localized", for example. And new users tend to ask a lot of highly closable questions, until they figure out the customs of SE sites.)

5. You could try and get an appropriate site started through Area 51, but this does not seem to be supported. The Area 51 FAQ states:

 > **Can I use Stack Exchange to support my product?**
 > 
 > Stack Exchange does not offer a private label service for owning a Q&A site. You are free to create an expert Q&A site in your area of expertise. There is a lot of visibility and credibility to becoming a central figure in an expert community, but Stack Exchange is a product for the Internet community at large, **not for corporations or individuals.** 

1. The Stack Exchange platform is no longer for sale or lease for this kind of thing, so you can't roll your own version that way.

2. There are a variety of clone platforms though. So you could create a support site that way and (re)write the API to allow posting questions and answers.

The short answer is "No".

This question has 3 parts:

1. Can the API list questions and answers about a product?
   Yes, if they are tagged and/or use keywords (like product numbers) that the API can search on.

2. Can the API be use to ask new questions?
   No. Officially, the API currently (version 2.1) does not support posting new questions or answers. This may change in the future, as alpha-stage API products appear to have write capability.

3. Are there any Stack Exchange sites that allow this?

4. I can't see any of the current Stack Exchange sites being very friendly to this kind of question. I imagine they'd get flagged and closed a lot.
   (They used to be considered "too localized", for example. And new users tend to ask a lot of highly closable questions, until they figure out the customs of SE sites.)

5. You could try and get an appropriate site started through Area 51, but this does not seem to be supported. The Area 51 FAQ states:

 > **Can I use Stack Exchange to support my product?**
 > 
 > Stack Exchange does not offer a private label service for owning a Q&A site. You are free to create an expert Q&A site in your area of expertise. There is a lot of visibility and credibility to becoming a central figure in an expert community, but Stack Exchange is a product for the Internet community at large, **not for corporations or individuals.** 

1. The Stack Exchange platform is no longer for sale or lease for this kind of thing, so you can't roll your own version that way.

2. There are a variety of clone platforms though. So you could create a support site that way and (re)write the API to allow posting questions and answers.