Is there any way by which we can have a hangout session within our webapp, say in an iframe ?
I was about to experiment with hangout api, but going by existing apps on hangout, it seems they can only be viewed and used from within Google+.
Is there a work around where I can make the user feel that hangout is a part of my app rather than my app being part of the hangout ?
There's no way to embed a hangout into your web application, but you can use the hangout button to launch a hangout app. This allows you to integrate features and data from your web application into a hangout.
The hangout button is made up of an image and a hangout launching link. It comes in a few sizes. Here's the code for the smallest size (75x19 px)
<a href="https://plus.google.com/hangouts/_?gid=APP_ID" style="text-decoration:none;">
<img src="https://ssl.gstatic.com/s2/oz/images/stars/hangout/1/gplus-hangout-15x79-normal.png"
alt="Start a Hangout"
style="border:0;width:79px;height:15px;"/>
</a>
In this snippet you must substitute APP_ID
with your application's ID from the API console. When you are viewing your project you'll find the application ID at the end of the URL.
Currently, there's no way of embedding a Hangout app in your web application. But, there's an opened issue tracker where you can add your comments about the need of this feature and Google might release it in their future API releases.