Im planning to develop a free facebook app. I need to know if its possible to have my app on user's wall?
Maybe like an icon or something. And when visitors of this user(my app's user) click this icon on his wall, this app should generate a jQuery popup and display some information.
Do you think it is possible? Does facebook allow third-party applications to be integrated right onto user wall?
Short answer is no. Facebook removed every app based profile page customization. If your app is a canvas app, your users can bookmark your app on their home page.
The most app-like output you can place in your user's facebook wall is a flash object, that could display anything you want and be interactive after the first click (think of the youtube videos that plays in timeline). If your users pin it on their timeline it will stay on top for two weeks. To post flash content to feeds, use the source attribe of the Post object.