I'm not sure why the Like is for the home page. If you look at the URL for the Like button on the home page, it specifically is calling out the correct page. I'm seeing 11k likes for the top 2 articles, but don't see any likes' for the home page specifically. I can't tell if these top 2 articles are 'linked' somehow, but if you have more information on how to test, please let us know.
As for the double image tags, that's fine. Facebook allows multiple image tags per page, but will take the first as the 'default' for that page. In some cases, where a user is asked which image to use, any of the image tags will be shown as an options. We always set overrides as the first image, so that shouldn't be a problem for normal likes. If you're seeing issues, let us know!
Thanks,
Alex