Right now, Google+ doesn’t seem to have much in the way of privacy settings. Here is what I am seeing:
1. Google will be deleting all private profiles. If you want to use Google+ you need to have a public profile which needs to include your name and gender. (Why gender, I wonder?)
2. Though you can choose to limit your posts, other people can share them. So there doesn’t seem to be, at this point, a way to control what you share. When you try to share a limited post Google does note that it is a limited post, but doesn’t stop the sharing.
3. You can share videos and you can limit with whom you share them, theoretically, but I am going to guess that other people can share your videos.
4. I tried to upload a video to my profile, but it doesn’t seem to actually upload it, or until I share it I can’t see it, not sure which. I really wish I could just upload it and then set privacy settings, instead of having to share it with people. I’d rather people can just come across it if they happen to be in a circle as opposed to my affirmatively sending a link.
Please note these aren’t really criticisms since Google is still in beta (testing.) Just notes on what I am seeing. I imagine things will change rapidly over the next few days and weeks.
As far as invitations, on occasion I get an invite button and other occasions there is nothing there. My ability to invite seems random. Also, even if I do invite someone, it can take days for the invitation to go through. If you want me to try to invite you I will, but no promises it will go through.
I’ll keep posting as I notice more.