1) The link for both the image and URL should be your full url:
yoursite.com/link-to-image.jpg. The domain should also be the same as your application. In other words, don't try to post an image from a different site or use a URL link to a different site.
2) The minimum dimensions I believe are 100x100px. I'd recommend something even larger, over 200x200px though as Facebook gives larger images more priority.
3) There should be a 2nd popup that appears that asks the user for permission to post on their behalf. It's not in the first popup that appears. The 2nd popup *can* be declined by the user. There is no way to force the user to allow posting to their feed on their behalf. That would be against Facebook's terms of service.
Hope that helps. If you still have issues, let us know. We'd need to be able to see the front-end of your site though to test if something may be configured wrong.
Thanks,
Alex