The Fan module is just for your Fan Page on Facebook. You're correct that you'll want to use the Like button for specific pages on your site.
When any Like button is clicked (for your Fan Page or for pages on your site), it will be entered into their Facebook Activity Log. From there, Facebook chooses how to show it in the Ticker, News Feed, or that user's Timeline based on different social factors. So, it's not guaranteed to show up in any of those, but the more clicks you get, the better the chances of your page(s) being seen.
As for a specific image, no, users can Like a specific image. What they can do is Like a specific page from your Gallery and then, you can set the Open Graph image tag for that page to be the image. Then, when a news feed is created for it, the link will go to that page, and the thumbnail image will be the gallery image. Facebook doesn't really like linking directly to an image only for various reasons.
To set the og:image tag, you can simply add the following tag in the gallery template:
{SCOpenGraph image=http://yoursite.com/link-to-image.jpg}You may need to add some PHP to that to dynamically set the image, but hope that gives you the idea and gets you started. Obviously, let us know if you have any questions.
Thanks,
Alex