I have experience with broadcasting and I have been trying to setup a podcast based on nerdy topics. Something like this could be easily done with skype, open broadcaster software, and twitch.tv. As far as people calling in? Hmm,... maybe over skype as like a guest on the show, but nothing really live. On Twitch there is a chat room that people can type into that should work as a "call in your question".
https://www.twitch.tv/kyotokombat/b/609288370
(You may want to fast forward it a bit)
^is an example of what it could look like, but instead of a video game playing we could set it up so it would show skype and the webcams of all in the call. If this was a live broadcast then to the right of the video there would be a chat room where anyone could ask a question to the host(s).