when you click the like button, you are liking the page that it is on. Even though you are using anchors to target a specific section of the page in the link back to the site, it is still the overall page that is being liked.
you wont be able to have a different image for each like button on the page, it will use only one image and title in the news feed.
you can set the image that will be used in the news feed by adding the following tag to your page in the head:
<link rel="image_src" href="http://mydomain.com/image.jpg" />