There looks to be a few issues going on here, but you're doing great so far :)

1. She won't appear in your Chat list unless you have her email address, or you meet the conditions outlined here: http://support.google.com/plus/bin/answer.py?hl=en&answer=1719476

2. There could be a number of reasons why you didn't hear her, but it would be important that she made sure she was not muted and that you could hear the test sounds, as outlined here: http://support.google.com/plus/bin/answer.py?hl=en&answer=1355579

3. On mobile, you're able to join an existing hangout from the stream [which you did], or you can start one from within Messenger (start a messenger conversation with that person, and then you can start a hangout].  You can't start a hangout in the stream from mobile.

Hope that helps!

Katherine