1) Can you tell us what setting you are using in EasySocial for this? We don't currently look at every setting possible within ES during the registration process, so it's likely just something we don't support yet. To be sure, are you adding the user to a user group (like registered, admin, etc) or to a Group page within EasySocial? Also, are you expecting *all* users to go into that group, or just ones that register with a social account?
That will help us understand more.
2) Google+ doesn't have any way to automatically detect if the avatar they are sending us for a user is a real avatar or if it's that blue shadow default one. We have a method that *tries* to guess if it's the default based on the size of the image that's returned. However, Google changes their default a lot (even a one pixel difference or just re-saving it on their end with different compression changes it), which means our method isn't always up to date.
Unfortunately, that behavior with Google+ is just something that happens and there's no way around it if you want to try and import the user's actual avatar. Google, of course, isn't updating Google+ anymore, so I don't expect any improvements to their API soon.
I hope that helps explain what you're seeing, at least, even if it doesn't really help with either issue for now.
Thanks,
Alex