Gmail – How to see who is online with the new “Hangouts” in Gmail

I have had this same issue on webinars and the best solution I came up with was to log in with another account on another computer. You could similarly set it up with a second monitor

Another solution I used was if I had someone else online helping me, I had them sit in the hangout and text me the questions (or I would sit in and text it to them). It doesn't directly fix you issue, but that is how I solved it

It seems the issue might have been that the invitations were not being sent to Google accounts. However that changed (Jason Lederman November 19, 2015) :

Users of Google Hangouts, Google’s video conferencing app, have long complained that only those with Gmail or Google+ accounts could use the service. Google answered those complaints today by introducing a “guest” mode, which will allow hosts to invite anyone to a Hangouts session. Hangouts organizers still need a Google account. But once they launch their Hangout, they can invite “external guests” (that's the term Google is using for anyone without a Google account) to join the conference via Google Calendar. The guest(s) will click on a link in the invitation, enter their name when prompted and can start chatting without creating accounts on Gmail or the newly-renovated Google+.

External guests can join on any web or mobile platform, and have to be approved (and can be kicked out at any time) by the organizer. The feature is still rolling out, so if you can’t access it yet, you’ll should be able to by the end of the week.