Andro,
It helps if you can post (or private message) us a link to a page that's having the problem. My guess from your description is that the Open Graph tags on that page aren't quite right. If you've set a default URL in the Open Graph area, that URL will be used as the Open Graph tag, then that URL will be used for all pages.. even if you specify a different URL in the {JFBCLike} tag. That's because Facebook will look at the URL in the Like tag, see the 'new' OG url that's specified, and then go use it's data for when the Like is clicked.
Hope that helps, but if that's not the issues, just let us know, and we can figure out a better answer
As for the image, I'm a little confused as to exactly what your looking for. I just registered on the site, and the Login module looks good to me. The image will always be a square, and always the same size (I think it's 50x50 if you choose small). With this, you can set the margin on the left and right so that it's always centered in the area you have for the login module. The center tag is never a perfect solution for images as it doesn't always work the same in each browser.
Good luck, and let us know if this helps you make any progress!