1. We don't have Google+ turned on for our domain. Would we still be able to authenticate against Google?
We don't have an option to disable Google+ authentication. However, we do have an option to allow Google authentications for user's that don't have a G+ account.
2. If yes to #1, would we be able to restrict logins to a single domain? It's for an internal site, and we don't want anyone outside our domain to have access.
Unfortunately, this isn't something we have built-in. However, if you wanted to only enable Google authentication, it would be relatively easy to add a few lines of code to check new users that are registering for their email domain and not allow it if it doesn't match.
The other option is to simply require administrator activation on new user accounts. Then, if someone tries to register that shouldn't be allowed, the admin just won't approve the account.
I hope that helps explain, but if you need anything else, just let us know.
Thanks,
Alex