It sounds like you want your users to make Facebook comments on items within your android app, much like they would use Facebook to leave comments on a non-Facebook website.
One way to do this is to authenticate users to Facebook, and allow them to leave comments which will be cached on your website or a visible server somewhere. These comments will be tagged with an ID unique to the user, and supplemented with their Profile Picture and Username, which will then link to Facebook itself. However, none of the comments will be visible on Facebook, only your app.
If you want to use Facebook as an unofficial ad platform, you can create a Facebook app which collects data from your Android app, and allow users to post Open Graph Stories about your products to Facebook.
In order to do this, you will need to authenticate your users to Facebook via your app, then configure your app to allow to post on their behalf regarding the item in your Android app.
Essentially, when a website allows users authenticated to Facebook to leave comments, what they are doing is identifying users via their Facebook credentials, however the comments are stored on the website, not Facebook itself. You'll need some way to store these comments on the web in order for your Android app to show this data to other users.