Just noticed this post in the wrong section. We moved it to the JFBC Pre-sales area, and hopefully, the answer below is what you're looking for.
We definitely support K2 integration for both profile import (you can select which fields from the user's profile are imported into each K2 field) and Open Graph integration. We have the option to automatically select the first image from a K2 or Joomla article and use as the image for Likes or Comments, as well as being able to specify the image specifically with our Open Graph tags per page. For more information on either of these, see the documentation below:
Open Graph integration for Joomla
Facebook profile integration for Joomla
The last link actually describes Community Builder profile integration, but the information is pretty much the same for the K2 integration as far as options go.
Hope that helps, and sorry again for the delay.
Thanks,
Alex