I have just made an iOS app that can share to Facebook. The Facebook post correctly shows that my sharing is coming from my app and shows \"1 hours ago via MYAPP\". The name of
I am not sure the link will bring you to the iTunes download page. According to my experience, that link will take you to the app's profile page on Facebook.
Something was changed since 1st Feb, 2012 that Facebook will not create profile page for new app by default. Please refer to this article - http://developers.facebook.com/blog/post/611/
However, you can manually create the profile page by going to "App Details > Contact Info", and then click the "Create Facebook Page" button as described in the article above.