Ratna,
There's a few ways to set the image for a page when the Like button is clicked:
* If there's a Open Graph plugin available for the extension that is rendering the page, like Joomla Content, K2 Content, EasyBlog, etc, install and enable that plugin. It should automatically select an image on the page for the Like button
* Add the {SCOpenGraph image=http://yoursite.com/link-to-image.jpg} on the page to set the image for that page. You can use PHP code to dynamically set the image as well.
* In the Open Graph -> Settings area, you can set a default image (like a logo) to be used site-wide if an image isn't specifically set on a specific page.
As for a post action, there's a few ways to do that. I'm assuming you are (or have a) developer? Do you want to have a popup appear with a predefined message that the user can edit and then hit "Post" whenever the user submits a quiz or something? Or, do you want the post to automatically happen, like "John took a quiz" with a link to the quiz?
Let me know, and we can help you understand how to do it with JFBConnect.
Thanks,
Alex